Author: "Champs, Gravitation et Cordes" - Searchworks@Jio Institute Digital Library Search Results

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86 results on '"Champs, Gravitation et Cordes"'

1. Rational Lax Matrices from Antidominantly Shifted Extended Yangians: BCD Types

Author: Rouven Frassek, Alexander Tsymbaliuk, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Nonlinear Sciences - Exactly Solvable and Integrable Systems, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Mathematics, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Representation Theory (math.RT), Exactly Solvable and Integrable Systems (nlin.SI), Mathematics::Representation Theory, Mathematics - Representation Theory, Mathematical Physics
Abstract: Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we construct a family of $SO(2r),Sp(2r),SO(2r+1)$ rational Lax matrices, polynomial in the spectral parameter, parametrized by the divisors on the projective line with coefficients being dominant integral coweights of associated Lie algebras. To this end, we provide the RTT realization of the antidominantly shifted extended Drinfeld Yangians of $\mathfrak{so}_{2r}, \mathfrak{sp}_{2r}, \mathfrak{so}_{2r+1}$, and of their coproduct homomorphisms. This establishes some of the recent conjectures in the physics literature by Costello-Gaiotto-Yagi (arXiv:2103.01835) in the classical types., Comment: v3: 67 pages, minor corrections, details added. v2: 65 pages, minor corrections, some details added, Remark 4.37 added. v1: 64 pages, comments are welcome!
Published: 2022
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2. Mesoscopic Klein-Schwinger effect in graphene

Author: A. Schmitt, P. Vallet, D. Mele, M. Rosticher, T. Taniguchi, K. Watanabe, E. Bocquillon, G. Fève, J. M. Berroir, C. Voisin, J. Cayssol, M. O. Goerbig, J. Troost, E. Baudin, B. Plaçais, Physique Mésoscopique, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire Ondes et Matière d'Aquitaine (LOMA), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Carbon - IEMN (CARBON - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), National Institute for Materials Science (NIMS), Physikalisches Institut [Köln], Universität zu Köln = University of Cologne, Nano-Optique, Laboratoire de Physique des Solides (LPS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Champs, Gravitation et Cordes, AcknowledgementsThe research leading to these results has received partial funding from the European Union Horizon 2020 research and innovation programme under Grant Agreement No. 881603 Graphene Core 3 (D.M., M.R., E. Baudin, B.P.). P.V. and J.C. were supported by the 'LIGHT S&T Graduate Program' (PIA3 Investment for the Future Program, ANR17-EURE-0027) and GPR LIGHT., ANR-17-EURE-0027,LIGHTS&T,University of Bordeaux Graduate Scholl in Light Sciences & Technologies(2017), European Project: 881603,H2020,H2020-SGA-FET-GRAPHENE-2019, GrapheneCore3(2020), Laboratoire Ondes et Matière d'Aquitaine [LOMA], Carbon - IEMN [CARBON - IEMN], Laboratoire de physique de l'ENS - ENS Paris [LPENS], National Institute for Materials Science [NIMS], and Laboratoire de Physique des Solides [LPS]
Subjects: High Energy Physics - Theory, Condensed Matter - Mesoscale and Nanoscale Physics, High Energy Physics - Theory (hep-th), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), General Physics and Astronomy, FOS: Physical sciences, [PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall]
Abstract: Strong electric field annihilation by particle-antiparticle pair creation, also known as the Schwinger effect, is a non-perturbative prediction of quantum electrodynamics. Its experimental demonstration remains elusive, as threshold electric fields are extremely strong and beyond current reach. Here, we propose a mesoscopic variant of the Schwinger effect in graphene, which hosts Dirac fermions with an approximate electron-hole symmetry. Using transport measurements, we report on universal 1d-Schwinger conductance at the pinchoff of ballistic graphene transistors. Strong pinchoff electric fields are concentrated within approximately 1 $\mu$m of the transistor's drain, and induce Schwinger electron-hole pair creation at saturation. This effect precedes a collective instability toward an ohmic Zener regime, which is rejected at twice the pinchoff voltage in long devices. These observations advance our understanding of current saturation limits in ballistic graphene and provide a direction for further quantum electrodynamic experiments in the laboratory., Comment: 39 pages, 13 figures, final version with extended discussion of the pinchoff effect in supplementary informations, abstract updated
Published: 2023
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3. Phases of holographic interfaces

Author: Constantin Bachas, Vassilis Papadopoulos, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, Phase transition, Black Holes, FOS: Physical sciences, Conformal map, General Relativity and Quantum Cosmology (gr-qc), QC770-798, AdS-CFT Correspondence, Conformal and W Symmetry, 01 natural sciences, General Relativity and Quantum Cosmology, Gravitation, Physics::Fluid Dynamics, Domain wall (string theory), Intersection, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, 010306 general physics, Condensed Matter - Statistical Mechanics, Physics, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Horizon, 81T35, Black hole, AdS/CFT correspondence, Classical mechanics, High Energy Physics - Theory (hep-th), Classical Theories of Gravity
Abstract: We compute the phase diagram of the simplest holographic bottom-up model of conformal interfaces. The model consists of a thin domain wall between three-dimensional Anti-de Sitter (AdS) vacua, anchored on a boundary circle. We distinguish five phases depending on the existence of a black hole, the intersection of its horizon with the wall, and the fate of inertial observers. We show that, like the Hawking-Page phase transition, the capture of the wall by the horizon is also a first order transition and comment on its field-theory interpretation. The static solutions of the domain-wall equations include gravitational avatars of the Faraday cage, black holes with negative specific heat, and an intriguing phenomenon of suspended vacuum bubbles corresponding to an exotic interface/anti-interface fusion. Part of our analysis overlaps with recent work by Simidzija and Van Raamsdonk but the interpretation is different., Comment: 57 pages, 14 figures. Minor changes
Published: 2021

4. 3D Ising model: a view from the conformal bootstrap island

Author: Slava Rychkov, Institut des Hautes Etudes Scientifiques (IHES), IHES, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, invariance: conformal, bootstrap: conformal, dimension: 3, Critical phenomena, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, General Physics and Astronomy, Conformal map, Parameter space, 01 natural sciences, 010305 fluids & plasmas, Conformal symmetry, Mathematics - Quantum Algebra, Ising model, 0103 physical sciences, FOS: Mathematics, Quantum Algebra (math.QA), correlation function, Statistical physics, 010306 general physics, Mathematical Physics, Condensed Matter - Statistical Mechanics, Mathematics, field theory: conformal, Statistical Mechanics (cond-mat.stat-mech), Conformal field theory, Probability (math.PR), Mathematical Physics (math-ph), critical phenomena, 16. Peace & justice, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Correlation function (statistical mechanics), High Energy Physics - Theory (hep-th), Critical exponent, Mathematics - Probability
Abstract: We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space., Comment: 16 pages, 3 figures, accepted for publication by C.R.Physique
Published: 2020
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5. Disc partition function of 2d R 2 gravity from DWG matrix model

Author: Kazakov, Vladimir, Levkovich-Maslyuk, Fedor, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Interdisciplinary Scientific Center Poncelet (ISCP), Independent University of Moscow (IUM)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institute for Information Transmission Problems, Russian Academy of Sciences [Moscow] (RAS), SCOAP3 (Sponsoring Consortium for Open Access Publishing in Particle Physics), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, defect, Matrix Models, topology, Statistical Mechanics (cond-mat.stat-mech), partition function, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], matrix model: duality, Feynman graph, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, QC770-798, Mathematical Physics (math-ph), singularity, boundary condition, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), quantum gravity, Nuclear and particle physics. Atomic energy. Radioactivity, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], dimension: 2, Condensed Matter - Statistical Mechanics, Mathematical Physics, 2D Gravity
Abstract: We compute the sum over flat surfaces of disc topology with arbitrary number of conical singularities. To that end, we explore and generalize a specific case of the matrix model of dually weighted graphs (DWG) proposed and solved by one of the authors, M. Staudacher and Th. Wynter. Namely, we compute the sum over quadrangulations of the disc with certain boundary conditions, with parameters controlling the number of squares (area), the length of the boundary and the coordination numbers of vertices. The vertices introduce conical defects with angle deficit given by a multiple of $\pi$, corresponding to positive, zero or negative curvature. Our results interpolate between the well-known 2d quantum gravity solution for the disc with fluctuating 2d metric and the regime of 'almost flat' surfaces with all the negative curvature concentrated on the boundary. We also speculate on possible ways to study the fluctuating 2d geometry with $AdS_2$ background instead of the flat one., Comment: 43 pages, 3 figures
Published: 2022
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6. A Flow in the Forest

Author: Gorsky, Alexander, Kazakov, Vladimir, Levkovich-Maslyuk, Fedor, Mishnyakov, Victor, HEP, INSPIRE, Institute for Information Transmission Problems, Russian Academy of Sciences [Moscow] (RAS), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and P. N. Lebedev Physical Institute of the Russian Academy of Sciences [Moscow] (LPI RAS)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, partition function, gravitation: model, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, matter: coupling, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], Condensed Matter - Statistical Mechanics, Mathematical Physics, lattice, perturbation theory, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], scaling, matter: conformal, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], potential: nonpolynomial, boundary condition, fermion: spinless, condensation, High Energy Physics - Theory (hep-th), quantum gravity, flow, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], [PHYS.COND] Physics [physics]/Condensed Matter [cond-mat]
Abstract: Using the matrix-forest theorem and the Parisi-Sourlas trick we formulate and solve a one-matrix model with non-polynomial potential which provides perturbation theory for massive spinless fermions on dynamical planar graphs. This is a lattice version of 2d quantum gravity coupled to massive spinless fermions. Our model equivalently describes the ensemble of spanning forests on the same graphs. The solution is formulated in terms of an elliptic curve. We then focus on a near-critical scaling limit when both the graphs and the trees in the forests are macroscopically large. In this limit we obtain universal one-point scaling functions (condensates), parameterized in terms of the Lambert function. Our results provide a rare example where one can explore the flow between two gravity models -- in this case, the theories of conformal matter coupled to 2d gravity with c=-2 (large trees regime) and c=0 (small trees regime). We also compute the disc partition functions with Dirichlet and Neumann boundary conditions in the same critical limit., 49 pages; v2: results on phi^3 correlator added, minor corrections
Published: 2022
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7. Steady states of holographic interfaces

Author: Constantin Bachas, Vassilis Papadopoulos, Zhongwu Chen, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, Phase transition, Black Holes, Event horizon, FOS: Physical sciences, Boundary (topology), General Relativity and Quantum Cosmology (gr-qc), QC770-798, AdS-CFT Correspondence, 01 natural sciences, General Relativity and Quantum Cosmology, membrane model, black hole: BTZ, Entropy (classical thermodynamics), Thermal conductivity, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, horizon: geometry, 0101 mathematics, dimension: 2, 010306 general physics, Quantum, Condensed Matter - Statistical Mechanics, field theory: conformal, Physics, Conformal Field Theory, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Horizon, 010102 general mathematics, critical phenomena, duality: holography, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Classical mechanics, High Energy Physics - Theory (hep-th), Flow (mathematics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], interface, entropy, Classical Theories of Gravity
Abstract: We find stationary thin-brane geometries that are dual to far-from-equilibrium steady states of two-dimensional holographic interfaces. The flow of heat at the boundary agrees with the result of CFT and the known energy-transport coefficients of the thin-brane model. We argue that by entangling outgoing excitations the interface produces coarse-grained entropy at a maximal rate, and point out similarities and differences with double-sided black funnels. The non-compact, non-Killing and far from-equilibrium event horizon of our solutions coincides with the local (apparent) horizon on the colder side, but lies behind it on the hotter side of the interface. We also show that the thermal conductivity of a pair of interfaces jumps at the Hawking-Page phase transition from a regime described by classical scatterers to a quantum regime in which heat flows unobstructed., 40 pages, 8 figures Added few discussion paragraphs
Published: 2021
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8. Linear-in-<math><mi>T</mi></math> resistivity from semiholographic non-Fermi liquid models

Author: Giuseppe Policastro, Benoît Douçot, Sutapa Samanta, Ayan Mukhopadhyay, Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, electron, FOS: Physical sciences, Scaling dimension, 01 natural sciences, Condensed Matter - Strongly Correlated Electrons, Fermi liquid, Electrical resistivity and conductivity, 0103 physical sciences, Effective field theory, temperature dependence, dimension: 2, fermion: operator, 010306 general physics, scaling: dimension, Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed matter physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Operator (physics), quasiparticle, temperature, Propagator, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), Quasiparticle, holography, propagator, Fermi liquid theory, liquid: model, Dimensionless quantity
Abstract: We construct a semiholographic effective theory in which the electron of a two-dimensional band hybridizes with a fermionic operator of a critical holographic sector, while also interacting with other bands that preserve quasiparticle characteristics. Besides the scaling dimension $\nu$ of the fermionic operator in the holographic sector, the effective theory has two {dimensionless} couplings $\alpha$ and $\gamma$ determining the holographic and Fermi-liquid-type contributions to the self-energy respectively. We find that irrespective of the choice of the holographic critical sector, there exists a ratio of the effective couplings for which we obtain linear-in-$T$ resistivity for a wide range of temperatures. This scaling persists to arbitrarily low temperatures when $\nu$ approaches unity in which limit we obtain a marginal Fermi liquid with a specific temperature dependence of the self-energy., Comment: Derivation of Green's function is included in the appendix. Minor revision in the main text
Published: 2021
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9. Exact solution of an integrable non-equilibrium particle system

Author: Rouven Frassek, Cristian Giardina', Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, noncompact, Statistical Mechanics (cond-mat.stat-mech), Nonlinear Sciences - Exactly Solvable and Integrable Systems, Probability (math.PR), [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Heisenberg model, integrability, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], particle: interaction, inverse scattering method, High Energy Physics - Theory (hep-th), FOS: Mathematics, duality, solution: nonperturbative, Exactly Solvable and Integrable Systems (nlin.SI), Condensed Matter - Statistical Mechanics, Mathematics - Probability, Mathematical Physics, spin: chain
Abstract: We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion process, the number of particles at each site is unbounded. We show that a finite chain of $N$ sites connected at its ends to two reservoirs can be solved exactly, i.e. the factorial moments of the non-equilibrium steady-state can be written in closed form for each $N$. The solution relies on probabilistic arguments and techniques inspired by integrable systems. It is obtained in two steps: i) the introduction of a dual absorbing process reducing the problem to a finite number of particles; ii) the solution of the dual dynamics exploiting a symmetry obtained from the Quantum Inverse Scattering Method. Long-range correlations are computed in the finite-volume system. The exact solution allows to prove by a direct computation that, in the thermodynamic limit, the system approaches local equilibrium. A by-product of the solution is the algebraic construction of a direct mapping between the non-equilibrium steady state and the equilibrium reversible measure., 45 pages, 2 figures, v2: minor improvements
Published: 2022
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10. Navigator function for the conformal bootstrap

Author: Slava Rychkov, David Simmons-Duffin, Marten Reehorst, Ning Su, Balt C. van Rees, Benoit Sirois, Institut des Hautes Etudes Scientifiques (IHES), IHES, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Institut des Hautes Études Scientifiques (IHES), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, California Institute of Technology (CALTECH), University of Pisa - Università di Pisa, École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), European Project: 758903,CFT-MAP, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, bootstrap: conformal, Current (mathematics), Property (programming), Computer science, QC1-999, FOS: Physical sciences, General Physics and Astronomy, Conformal map, Space (mathematics), 01 natural sciences, numerical methods, Ising model, 0103 physical sciences, numerical calculations, 010306 general physics, Condensed Matter - Statistical Mechanics, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Physics, Function (mathematics), Standard methods, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), Optimization methods, higher-dimensional, Algorithm
Abstract: Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are everywhere well-defined, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island., 60 pages, 22 figures. v2: minor changes and fixes, added subsection 3.1 on differentiability
Published: 2021
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11. Glue-and-cut at five loops

Author: Vladimir A. Smirnov, Raul Pereira, Erik Panzer, Vasco Goncalves, Alexander V. Smirnov, Alessandro Georgoudis, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Paris Cité, Uppsala University, Faculdade de Ciências da Universidade do Porto, Universidade Estadual Paulista (UNESP), University of Oxford, Trinity College Dublin, Moscow State University, Moscow Center for Fundamental and Applied Mathematics, and Skobeltsyn Institute of Nuclear Physics of Moscow State University
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, FOS: Physical sciences, Position and momentum space, QC770-798, field theory, 01 natural sciences, Set (abstract data type), Subatomär fysik, Dimensional regularization, High Energy Physics - Phenomenology (hep-ph), Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, Subatomic Physics, Perturbative QCD, regularization: dimensional, 010306 general physics, Scattering Amplitudes, Physics, loop integral, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Mathematical analysis, Feynman graph: higher-order, perturbation theory: higher-order, Propagator, Order (ring theory), mathematical methods, Scattering amplitude, Massless particle, High Energy Physics - Phenomenology, High Energy Physics - Theory (hep-th), [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], master integral, Renormalization Regularization and Renormalons, epsilon expansion
Abstract: We compute epsilon-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of transcendental weight nine. Our method is the glue-and-cut technique from Baikov and Chetyrkin, which proves extremely effective in that it determines all expansion coefficients to this order in terms of recursively one-loop integrals and only one further integral. We observe that our results are compatible with conjectures that predict $\pi$-dependent contributions., Comment: 20 pages, 8 figures
Published: 2021
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12. Tensor RG approach to high-temperature fixed point

Author: Tom Kennedy, Slava Rychkov, Institut des Hautes Etudes Scientifiques (IHES), IHES, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el), 82B28 (Primary) 82B27, 82B20 (Secondary), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), critical phenomena, tensor, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory (hep-th), fixed point, network, Ising model, renormalization group, dimension: 2, Mathematical Physics, Condensed Matter - Statistical Mechanics, lattice
Abstract: We study a renormalization group (RG) map for tensor networks that include two-dimensional lattice spin systems such as the Ising model. Numerical studies of such RG maps have been quite successful at reproducing the known critical behavior. In those numerical studies the RG map must be truncated to keep the dimension of the legs of the tensors bounded. Our tensors act on an infinite-dimensional Hilbert space, and our RG map does not involve any truncations. Our RG map has a trivial fixed point which represents the high-temperature fixed point. We prove that if we start with a tensor that is close to this fixed point tensor, then the iterates of the RG map converge in the Hilbert-Schmidt norm to the fixed point tensor. It is important to emphasize that this statement is not true for the simplest tensor network RG map in which one simply contracts four copies of the tensor to define the renormalized tensor. The linearization of this simple RG map about the fixed point is not a contraction due to the presence of so-called CDL tensors. Our work provides a first step towards the important problem of the rigorous study of RG maps for tensor networks in a neighborhood of the critical point., Comment: version 2: The exposition of the proof of proposition 2.3 has been expanded. version 3 (this version): A minor error in the first paragraph of the proof of Lemma 2.1 has been corrected and figure 2.55 has been replaced as part of this correction
Published: 2021

13. Massive AdS supergravitons and holography

Author: Constantin Bachas, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), and École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: High Energy Physics - Theory, invariance: conformal, Nuclear and High Energy Physics, Superstring Vacua, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), AdS-CFT Correspondence, String theory, 01 natural sciences, symmetry: global, General Relativity and Quantum Cosmology, decoupling, High Energy Physics::Theory, Poincare, space-time: anti-de Sitter, Bimetric gravity, 0103 physical sciences, Effective field theory, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, 010306 general physics, Mathematical physics, Physics, field theory: conformal, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Graviton, deformation, Supersymmetry, Global symmetry, Moduli space, AdS/CFT correspondence, High Energy Physics - Theory (hep-th), gravitation, graviton, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], lcsh:QC770-798, holography, supersymmetry
Abstract: I compare two holographic mechanisms giving to the graviton a parametrically-small supersymmetric mass $m_g$ in Anti-de Sitter spacetime. In the context of bi-metric gravity these mechanisms couple `weakly' two initially decoupled superconformal theories by: (i) turning on a double-trace deformation, or (ii) gauging a common global symmetry. Superconformal invariance restricts the number of Poincar\'e supercharges to $N_Q\leq 4$ for mechanism (i) and to $N_Q\leq 8$ for mechanism (ii), and the AdS dimension to $D\leq 5$. The putative effective supergravities are expected to break down in the $m_g\to 0$ limit at an intermediate scale between $ m_g$ and $m_{\rm Planck}$. In a recently-proposed microscopic embedding of mechanism (ii) in string theory I show that $m_g=0$ is at infinite distance in moduli space, and I relate the breakdown of the effective theory to the condensation of unprotected spin-2 excitations in the string-theoretic description of the `holographic bridge'. The phenomenon is invisible in the weakly-coupled CFT side. I conjecture that similar phenomena should be at work in all cases., Comment: 19 pages, one figure. Minor corrections and amendments. Version to be published in JHEP
Published: 2019
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14. Exact holographic RG flows and the A1 × A1 Toda chain

Author: Irina Ya. Aref'eva, Anastasia A. Golubtsova, Giuseppe Policastro, Observatoire de Paris, Université Paris sciences et lettres (PSL), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: Physics, Nuclear and High Energy Physics, Field (physics), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Equations of motion, Boundary (topology), Fixed point, AdS-CFT Correspondence, 01 natural sciences, Gauge-gravity correspondence, AdS/CFT correspondence, Flow (mathematics), 0103 physical sciences, Black brane, lcsh:QC770-798, Dilaton, Holography and quark-gluon plasmas, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Mathematical physics
Abstract: We construct analytic solutions of Einstein gravity coupled to a dilaton field with a potential given by a sum of two exponentials, by rewriting the equations of motion in terms of an integrable Toda chain. These solutions can be interpreted as domain walls interpolating between different asymptotics, and as such they can have interesting applications in holography. In some cases, we can construct a solution which interpolates between an AdS fixed point in the UV limit and a hyperscaling violating boundary in the IR region. We also find analytic black brane solutions at finite temperature. We discuss the properties of the solutions and the interpretation in terms of RG flow.
Published: 2019
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15. A new dual system for the fundamental units including and going beyond the newly revised SI

Author: Pierre Fayet, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Permittivity, FOS: Physical sciences, Energy Engineering and Power Technology, Joule, Elementary charge, 7. Clean energy, 01 natural sciences, 010305 fluids & plasmas, High Energy Physics - Phenomenology (hep-ph), Physics - General Physics, Quantum mechanics, Magnetic flux quantum, 0103 physical sciences, Coulomb, Ohm, 010306 general physics, Ampere, activity report, Physics, scaling, General Engineering, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Phenomenology, General Physics (physics.gen-ph), fundamental constant, Dimensionless quantity
Abstract: We propose a new system for the fundamental units, which includes and goes beyond the present redefinition of the SI, by choosing also $c=\hbar=1$. By fixing $c=c_\circ $m/s = 1, $\hbar=\hbar_\circ $ Js = 1 and $\underline{\mu_\circ}=\mu_\circ $N/A$^2$ = 1, it allows us to define the metre, the joule, and the ampere as equal to (1/299 792 458) s, $(1/\hbar_\circ = .948 ... \times \ 10^{34})\ {\rm s}^{-1}$ and $\sqrt{\mu_\circ \rm N}= \sqrt{\mu_\circ c_\circ / \hbar_\circ}\ {\rm s}^{-1}= 1.890...\times 10^{18}\ {\rm s}^{-1}$. It presents at the same time the advantages and elegance of a system with $\hbar = c = \underline{\mu_\circ} = \underline{\epsilon_\circ } = k = N_A = 1\,$, where the vacuum magnetic permeability, electric permittivity, and impedance are all equal to 1. All units are rescaled from the natural ones and proportional to the s, s$^{-1}$, s$^{-2}$, ... or just 1, as for the coulomb, ohm and weber, now dimensionless. The coulomb is equal to $\sqrt{\mu_\circ c_\circ / \hbar_\circ}= 1.890... \times 10^{18}$, and the elementary charge to $e=1.602...\times 10^{-19} {\rm C} = \sqrt{4\pi\alpha}=.3028... $ . The ohm is equal to $1/\mu_\circ c_\circ$ so that the impedance of the vacuum is $Z_\circ = 376.730... \Omega =1$. The volt is $ 1/ \sqrt{{\mu_\circ c_\circ \hbar_\circ}}\ {\rm s}^{-1} = 5.017... \times\ 10^{15}\ {\rm s}^{-1}$, and the tesla $c_\circ $V/m = $ \sqrt{{c_\circ^3}/{\mu_\circ\hbar_\circ}}\ {\rm s}^{-2} = 4.509... \times 10^{32}\ {\rm s}^{-2}$. The weber is $ 1/ \sqrt{{\mu_\circ c_\circ \hbar_\circ}} = 5.017... \times\ 10^{15}$. $\ K_J =483\,597. \ $... GHz/V $= e/\pi = $ .09639..., and $R_K = 25\,812.\ ...\ \Omega =1/2\alpha\simeq 68.518$. One can also fix $e$ = 1.602 176 634 $\times 10^{-19}$ C, at the price of adjusting the coulomb and all electrical units with $\mu_\circ=4\pi\times 10^{-7}\eta^2$ where $\eta^2, \propto \alpha$, is very close to 1., Comment: 26 pages, 2 tables
Published: 2019
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16. Superstrings in Thermal Anti-de Sitter Space

Author: Sujay K. Ashok, Jan Troost, Homi Bhabha National Institute (HBNI), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, partition function, dimension: 3, superstring, Casimir, FOS: Physical sciences, torus: twist, off-shell, AdS-CFT Correspondence, String theory, 01 natural sciences, 010305 fluids & plasmas, Conformal dimension, thermal, High Energy Physics::Theory, space-time: anti-de Sitter, 0103 physical sciences, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, ground state, modular, string model, 010306 general physics, Mathematical physics, Physics, Partition function (quantum field theory), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Hilbert space, group: isometry, free energy, Casimir effect, flux, AdS/CFT correspondence, High Energy Physics - Theory (hep-th), Conformal Field Models in String Theory, Path integral formulation, lcsh:QC770-798, dimension: conformal, Anti-de Sitter space, quantization, Isometry group, path integral, Ramond
Abstract: We revisit the calculation of the thermal free energy for string theory in three-dimensional anti-de Sitter spacetime with Neveu-Schwarz-Neveu-Schwarz flux. The path integral calculation is exploited to confirm the off-shell Hilbert space and we find that the Casimir of the discrete representations of the isometry group takes values in a half-open interval. We extend the free energy calculation to the case of superstrings, calculate the boundary toroidal twisted partition function in the Ramond-Ramond sector, and prove lower bounds on the boundary conformal dimension from the bulk perspective. We classify Ramond-Ramond ground states and construct their second quantized partition function. The partition function exhibits intriguing modular properties., Comment: 58 pages, 4 figures
Published: 2021
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17. Random field Ising model and Parisi-Sourlas supersymmetry. Part II. Renormalization group

Author: Slava Rychkov, Emilio Trevisani, Apratim Kaviraj, institut de Physique Théorique Philippe Meyer (IPM), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Institut des Hautes Etudes Scientifiques (IHES), IHES, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: dimension: 6, High Energy Physics - Theory, Nuclear and High Energy Physics, perturbation, FOS: Physical sciences, Fixed point, 01 natural sciences, anomalous dimension, High Energy Physics::Theory, random field, Ising model, 0103 physical sciences, dimensional reduction, Renormalization Group, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical physics, Physics, Random field, Conformal Field Theory, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Conformal field theory, High Energy Physics::Phenomenology, Random Systems, Disordered Systems and Neural Networks (cond-mat.dis-nn), Supersymmetry, Renormalization group, Condensed Matter - Disordered Systems and Neural Networks, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], fixed point, High Energy Physics - Theory (hep-th), multiplet, Dimensional reduction, renormalization group: flow, Supersymmetry and Duality, lcsh:QC770-798, High Energy Physics::Experiment, supersymmetry, Critical dimension
Abstract: We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric fixed point (Cardy, 1985), we look for interactions which may destabilize the SUSY RG flow and lead to the loss of dimensional reduction. This problem is reduced to studying the anomalous dimensions of "leaders" -- lowest dimension parts of $S_n$-invariant perturbations in the Cardy basis. Leader operators are classified as non-susy-writable, susy-writable or susy-null depending on their symmetry. Susy-writable leaders are additionally classified as belonging to superprimary multiplets transforming in particular $\textrm{OSp}(d | 2)$ representations. We enumerate all leaders up to 6d dimension $Δ= 12$, and compute their perturbative anomalous dimensions (up to two loops). We thus identify two perturbations (with susy-null and non-susy-writable leaders) becoming relevant below a critical dimension $d_c \approx 4.2$ - $4.7$. This supports the scenario that the SUSY fixed point exists for all $3 < d \leq 6$, but becomes unstable for $d < d_c$., 103 pages, 15 figures. v2: susy-null leader discussion modified (Sec. 8.5 and App. A.6), and other tweaks. v3: version accepted by JHEP, added executive summary in Sec. 1.1, discussion in Sec 11.1.1 and Sec. 11.2.1, corrected typos. v4: corrected typos. Conclusions unchanged
Published: 2021
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18. String Scale Thermal Anti-de Sitter Spaces

Author: Jan Troost, Sujay K. Ashok, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, FOS: Physical sciences, finite temperature, scale: string, QC770-798, AdS-CFT Correspondence, String theory, Curvature, 01 natural sciences, String (physics), thermal, High Energy Physics::Theory, space-time: anti-de Sitter, Conformal symmetry, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, ground state, Continuum (set theory), string model, 010306 general physics, circle, Orbifold, Mathematical physics, Physics, 010308 nuclear & particles physics, background, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], critical phenomena, free energy, AdS/CFT correspondence, AdS(3) x S(1), High Energy Physics - Theory (hep-th), symmetry: conformal, Conformal Field Models in String Theory, curvature, fractional, orbifold, Anti-de Sitter space, quantization, path integral
Abstract: We study finite temperature string scale $AdS_3$ backgrounds. One background is $AdS_3 \times S^1 \times T^2$ in which the anti-de Sitter space-time and the circle are at the radius $\sqrt{\alpha'}$. Using path integral techniques, we show that the bulk spectrum includes a continuum of states as well as Ramond-Ramond ground states that agree with those of the symmetric orbifold of the two-torus after second quantization. We also examine the one-loop free energy of the background $AdS_3 \times S^1$ at curvature radius $\sqrt{2 \alpha'/3}$. In the space-time NSNS sector, the string theory spontaneously breaks conformal symmetry as well as R-charge conjugation symmetry. We prove that the minimum in the boundary energy is reached for a singly wound string. In the RR sector, we classify the infinite set of ground states with fractional R-charges. Moreover, we remark on the behaviour of critical temperatures as the curvature scale becomes smaller than the string scale. In an appendix, we derive the Hawking-Page transition in string theory by integrating a world sheet one-point function., Comment: 20 pages
Published: 2021
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19. Thermal transport in TT -deformed conformal field theories: from integrability to holography

Author: Medenjak, Marko, Policastro, Giuseppe, Yoshimura, Takato, institut de Physique Théorique Philippe Meyer (IPM), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: [PHYS]Physics [physics]
Abstract: International audience; In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator TT , using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulae for these quantities in pure CFTs. We also compute the exact momentum diffusion constant using the integrability-based method, and confirm that it agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the TT-deformed CFTs. First of all, they provide the first check of the TTdeformed AdS3/CFT2 correspondence from the dynamical standpoint. And secondly, we are able to identify a remarkable connection between the TT-deformed CFTs and reversible cellular automata.
Published: 2021
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20. Gentle introduction to rigorous Renormalization Group: a worked fermionic example

Author: Alessandro Giuliani, Slava Rychkov, Vieri Mastropietro, Institut des Hautes Etudes Scientifiques (IHES), IHES, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Giuliani, Alessandro, Mastropietro, Vieri, Rychkov, Slava, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, Critical phenomena, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Banach space, kinetic, FOS: Physical sciences, Kinetic term, Fixed point, nonperturbative, 01 natural sciences, fermion: symplectic, Theoretical physics, 0103 physical sciences, Ising model, FOS: Mathematics, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, renormalization group: fixed point, Renormalization Group, 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical Physics, Quartic interaction, Physics, Statistical Mechanics (cond-mat.stat-mech), 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Probability (math.PR), nonlocal, Mathematical Physics (math-ph), critical phenomena, Renormalization group, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), Nonperturbative Effects, lcsh:QC770-798, Mathematics - Probability, Symplectic geometry
Abstract: Much of our understanding of critical phenomena is based on the notion of Renormalization Group (RG), but the actual determination of its fixed points is usually based on approximations and truncations, and predictions of physical quantities are often of limited accuracy. The RG fixed points can be however given a fully rigorous and non-perturbative characterization, and this is what is presented here in a model of symplectic fermions with a nonlocal ("long-range") kinetic term depending on a parameter $\varepsilon$ and a quartic interaction. We identify the Banach space of interactions, which the fixed point belongs to, and we determine it via a convergent approximation scheme. The Banach space is not limited to relevant interactions, but it contains all possible irrelevant terms with short-ranged kernels, decaying like a stretched exponential at large distances. As the model shares a number of features in common with $\phi^4$ or Ising models, the result can be used as a benchmark to test the validity of truncations and approximations in RG studies. The analysis is based on results coming from Constructive RG to which we provide a tutorial and self-contained introduction. In addition, we prove that the fixed point is analytic in $\varepsilon$, a somewhat surprising fact relying on the fermionic nature of the problem., Comment: 55 pages + appendices, many figures; v2: refs added; v3: refs added, intro greatly expanded, App. J.1 added, version accepted by JHEP; v4: minor misprints corrected
Published: 2021
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21. Effective gravitational action for 2D massive fermions

Author: Corinne de Lacroix, Harold Erbin, Adel Bilal, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Center for Theoretical Physics, Massachusetts Institute of Technology (MIT), NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), Département Intelligence Ambiante et Systèmes Interactifs (DIASI), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, European Project: 891169,ML4SFT, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, FOS: Physical sciences, QC770-798, Euclidean, Liouville, 01 natural sciences, Gravitation, Theoretical physics, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, Euclidean geometry, Models of Quantum Gravity, gravitation: action, 010306 general physics, expansion: mass, fermion: massive, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], nonlocal, Fermion, Manifold, Action (physics), High Energy Physics - Theory (hep-th), 2D Gravity
Abstract: We work out the effective gravitational action for 2D massive Euclidean fermions in a small mass expansion. Besides the leading Liouville action, the order $m^2$ gravitational action contains a piece characteristic of the Mabuchi action, much as for 2D massive scalars, but also several non-local terms involving the Green's functions and Green's functions at coinciding points on the manifold., Comment: 32 pages
Published: 2021
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22. Leading-color two-loop QCD corrections for three-jet production at hadron colliders

Author: S. Abreu, F. Febres Cordero, H. Ita, B. Page, V. Sotnikov, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), CERN Theoretical Physics Department, CERN [Genève], Department of Physics and Astronomy [UCLA, Los Angeles], University of California [Los Angeles] (UCLA), University of California (UC)-University of California (UC), Department of Physics [Tallahassee], Florida State University [Tallahassee] (FSU), Physikalisches Institut [Freiburg], Albert-Ludwigs-Universität Freiburg, Champs, Gravitation et Cordes, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) (MPI-P), ANR-17-CE31-0001,Amplitudes,Structures nouvelles pour les amplitudes de diffusion(2017), European Project: 725110,AMPLITUDES, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Nuclear and High Energy Physics, 010308 nuclear & particles physics, hadron: colliding beams, higher-order: 2, FOS: Physical sciences, hep-ph, QC770-798, QCD Phenomenology, 01 natural sciences, quantum chromodynamics: correction, 3. Good health, color, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), jet: multiple production, Nuclear and particle physics. Atomic energy. Radioactivity, NLO Computations, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], 0103 physical sciences, High Energy Physics::Experiment, 010306 general physics, numerical calculations, Particle Physics - Phenomenology
Abstract: We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation., Comment: Analytic results in ancillary files; link for numerical code in references. v3: matches the published version
Published: 2021
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23. Distributions in CFT. Part II. Minkowski space

Author: Jiaxin Qiao, Petr Kravchuk, Slava Rychkov, Institut des Hautes Etudes Scientifiques (IHES), IHES, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Champs, Gravitation et Cordes, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: space: Minkowski, invariance: conformal, Nuclear and High Energy Physics, Pure mathematics, tube, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Field Theories in Higher Dimensions, QC770-798, Conformal and W Symmetry, 01 natural sciences, operator product expansion, field theory: Euclidean, Conformal symmetry, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, Euclidean geometry, Minkowski space, Ising model, unitarity, correlation function, 010306 general physics, Commutative property, Axiom, Physics, field theory: conformal, Conformal Field Theory, 010308 nuclear & particles physics, Conformal field theory, axiomatic field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Wightman axioms, D Intuition about Lemma 4.2, 16. Peace & justice, spectral, Signature (topology), signature
Abstract: CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all Wightman axioms (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the s-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the s-channel OPE expansion in the radial cross-ratios ρ, $$ \overline{\rho} $$ ρ ¯ . We prove a key fact that |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ < 1 inside the forward tube, and set bounds on how fast |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ may tend to 1 when approaching the Minkowski space.We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and Osterwalder-Schrader (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).
Published: 2021
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24. The AdS$_{3}$ × S$^{1}$ chiral ring

Author: Songyuan Li, Sujay K. Ashok, Jan Troost, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Champs, Gravitation et Cordes, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: Nuclear and High Energy Physics, Structure constants, Worldsheet, High Energy Physics::Lattice, Boundary (topology), QC770-798, supersymmetry: 2, AdS-CFT Correspondence, String theory, 01 natural sciences, operator product expansion, High Energy Physics::Theory, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, Operator product expansion, string model, chiral ring, 010306 general physics, Mathematical physics, Physics, field theory: conformal, Ring (mathematics), flow: spectral, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Zero (complex analysis), operator: vertex, flux, AdS(3) x S(1), Conformal Field Models in String Theory, Vertex (curve)
Abstract: We study AdS3× S1× Y supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to $$ \mathcal{N} $$ N = 2 superconformal theories on the boundary. We classify all worldsheet vertex operators that correspond to space-time chiral primaries. We compute space-time chiral ring structure constants for operators in the zero spectral flow sector using the operator product expansion in the worldsheet theory. We find that the structure constants take a universal form that depends only on the topological data of the $$ \mathcal{N} $$ N = 2 superconformal theory on Y.
Published: 2021
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25. $U$ boson interpolating between a generalized dark photon or dark $Z$ , an axial boson, and an axionlike particle

Author: Fayet, Pierre, Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, scale: grand unified theory, longitudinal, High Energy Physics::Lattice, coupling: gauge, isovector, doublet: 2, FOS: Physical sciences, quark: chiral, dark matter, High Energy Physics - Experiment, High Energy Physics - Experiment (hep-ex), High Energy Physics - Phenomenology (hep-ph), parity: violation, photon: coupling, isoscalar, mixing, pseudoscalar, neutrino: interaction, High Energy Physics::Phenomenology, singlet, atomic physics: parity, symmetry: U(1), suppression, coupling: axial, High Energy Physics - Phenomenology, Beyond the standard model, High Energy Physics - Theory (hep-th), meson: decay, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], axion-like particles, High Energy Physics::Experiment
Abstract: A light boson $U$ from an extra $U(1)$ interpolates between a generalized dark photon coupled to $Q,\ B$ and $L_i$ (or $B-L$), plus possibly dark matter, a dark $Z$ coupled to the $Z$ current, and one axially coupled to quarks and leptons. We identify the corresponding $U(1)_F$ symmetries, with $F= \gamma_Y Y+\gamma_B B+\gamma_{L_i}L_i+\gamma_A F_A+\gamma_{F'}F'\!+\gamma_d F_d$, $F_d$ acting in a dark sector and $F'$ on possible semi-inert BEH doublets uncoupled to quarks and leptons. The $U$ current is obtained from the $U(1)_F $ and $Z$ currents, with a mixing determined by the spin-0 BEH fields. The charge $Q_U$ of chiral quarks and leptons is a combination of $Q,\ B,\ L_i$ and $T_{3L}$ with the axial $F_A$. It involves in general isovector and isoscalar axial terms, in the presence of two BEH doublets. A longitudinal $U$ with axial couplings has enhanced interactions, and behaves much as an axionlike particle. Its axial couplings $g_A$, usually restricted to $< 2\times 10^{-7} m_U$(MeV), lead to effective pseudoscalar ones $g_P= g_A\times 2m_{q,l}\,/m_U=2^{1/4}\, G_F^{1/2}\, m_{q,l} \ A_\pm $. $\,A_\pm$ is proportional to an invisibility parameter $r=\cos\theta_A$ induced by a singlet v.e.v., possibly large and allowing the $U$ to be very weakly interacting. This allows for a very small gauge coupling, expressed with two doublets and a singlet as $g"\!/4\simeq 2\times 10^{-6} m_U$(MeV) $ r/\sin 2\beta$. We discuss phenomenological implications for meson decays, neutrino interactions, atomic-physics parity violation, naturally suppressed $\pi^0\to\gamma U$ decays, etc.. The $U$ boson fits within the grand-unification framework, in symbiosis with a $SU(4)_{\rm es }$ electrostrong symmetry broken at the GUT scale, with $Q_U$ depending on $Q,\ B-L,\ F_A$ and $T_{3A}$ through three parameters $\gamma_Y,\ \gamma_A$ and $\eta$., Comment: 25 pages
Published: 2021
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26. Energy Reflection and Transmission at 2D Holographic Interfaces

Author: Giuseppe Policastro, Constantin Bachas, Shira Chapman, Dongsheng Ge, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Université de Paris (UP)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Université de Paris (UP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), String Theory (ITFA, IoP, FNWI), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, General Physics and Astronomy, FOS: Physical sciences, Conformal map, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, String (physics), General Relativity and Quantum Cosmology, Gravitation, Condensed Matter - Strongly Correlated Electrons, Quantum mechanics, 0103 physical sciences, Reflection coefficient, 010306 general physics, dimension: 2, initial state, Physics, field theory: conformal, Strongly Correlated Electrons (cond-mat.str-el), Conformal field theory, Scattering, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], scattering, duality: string, duality: holography, tension, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], flux, Reflection (mathematics), High Energy Physics - Theory (hep-th), gravitation, central charge, Elementary Particles and Fields, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], interface, Central charge, reflection
Abstract: Scattering from conformal interfaces in two dimensions is universal in that the flux of reflected and transmitted energy does not depend on the details of the initial state. In this letter, we present the first gravitational calculation of energy reflection and transmission coefficients for interfaces with thin-brane holographic duals. Our result for the reflection coefficient depends monotonically on the tension of the dual string anchored at the interface, and obeys the lower bound recently derived from the ANEC in conformal field theory. The B(oundary)CFT limit is recovered for infinite ratio of the central charges., Comment: 5 pages, 1 figure
Published: 2020
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27. Holographie topologique

Author: Li, Songyuan, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Champs, Gravitation et Cordes, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres, Jan Troost, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris)
Subjects: Topological quantum field theory, Théorie des cordes, AdS/CFT correspondence, [PHYS.PHYS]Physics [physics]/Physics [physics], [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Gravité quantique, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Quantum gravity, String theory, Correspondance AdS/CFT, Théorie quantique topologique des champs
Abstract: This thesis concentrates on the topologically twisted version of the AdS₃/CFT₂ correspondence. We start by studying the topologically twisted N=2 supersymmetric Liouville theory with massive deformations. We determine the chiral ring elements and compute their correlations functions. We then turn to define a three-dimensional gravity theory that is the holographic dual of Liouville theory. The action of this gravity theory is the same as the one of classical general relativity while the path integral measure is taken to be the same as the Liouville theory. We study in detail the properties of this gravity theory and then generalize it to the supersymmetric case where by changing the boundary conditions we find it dual to the topologically twisted N=2 supersymmetric Liouville theory mentioned above. The classical configurations corresponding to the chiral ring will be computed. Next, we turn to a string realization of the duality and analyze a string theory on the locally AdS₃ background with a conformally flat boundary. We find the boundary energy-momentum tensor becomes topological when we impose a specific coupling to the boundary metric given by the boundary conditions. Finally, we study the topological orbifold conformal field theories on the symmetric product of a complex surface M, which is the conjectured dual to the ten-dimensional string theory on AdS₃×S³×M.; Cette thèse porte sur la version topologiquement twistée de la correspondance AdS₃/CFT₂. Nous commençons par étudier la théorie de Liouville N=2 supersymétrique topologiquement twistée avec des déformations massives. Nous déterminons les éléments de l'anneau chiral et nous calculons leurs fonctions de corrélations. Nous définissons ensuite une théorie de la gravité à trois dimensions qui est le dual holographique de la théorie de Liouville. L'action de cette théorie de la gravité est la même que celle de la relativité générale classique tandis que la mesure de l'intégrale de chemin est la même que celle de la théorie de Liouville. Nous étudions en détail les propriétés de cette théorie de la gravité avant de généraliser au cas supersymétrique pour lequel, en changeant les conditions aux limites, nous observons qu'il est dual à la théorie de Liouville N=2 supersymétrique topologiquement twistée mentionnée précédemment. Les configurations classiques correspondant à l'anneau chiral seront calculées. Nous nous intéresserons ensuite à une réalisation de la dualité en termes de cordes et analysons une théorie de cordes sur un fond localement AdS₃ avec une frontière conformalement plate. Nous observons que le tenseur énergie-impulsion de la frontière devient topologique lorsque l'on impose un couplage spécifique à la métrique de la frontière donné par les conditions aux limites. Nous étudions finalement les théories topologiques conformes de champs d'orbifolds sur le produit symétrique d'une surface complexe M, qui est le dual conjecturé de la théorie des cordes à dix dimensions sur AdS₃×S³×M.
Published: 2020

28. $T\bar{T}$-deformed conformal field theories out of equilibrium

Author: Takato Yoshimura, Giuseppe Policastro, Marko Medenjak, institut de Physique Théorique Philippe Meyer (IPM), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: momentum: diffusion, High Energy Physics - Theory, Overline, Field (physics), FOS: Physical sciences, General Physics and Astronomy, Conformal map, integrability, 01 natural sciences, Reversible cellular automaton, Momentum diffusion, 0103 physical sciences, Connection (algebraic framework), 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical physics, Physics, field theory: conformal, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Order (ring theory), Cellular automaton, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], 3. Good health, High Energy Physics - Theory (hep-th), Elementary Particles and Fields, holography, cellular automaton
Abstract: We consider the out-of-equilibrium transport in $T\bar{T}$-deformed (1+1)-dimension conformal field theories (CFTs). The theories admit two disparate approaches, integrability and holography, which we make full use of in order to compute the transport quantities, such as the the exact non-equilibrium steady state currents. We find perfect agreements between the results obtained from these two methods, which serve as the first checks of the $T\bar{T}$-deformed holographic correspondence from the dynamical standpoint. It turns out that integrability also allows us to compute the momentum diffusion, which is given by a universal formula. We also remark on an intriguing connection between the $T\bar{T}$-deformed CFTs and reversible cellular automata., v1: 6 pages, 1 figure. v2: typos corrected, v3: Fig. 1 corrected, published version
Published: 2020
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29. Duality and hidden equilibrium in transport models

Author: Cristian Giardinà, Jorge Kurchan, Rouven Frassek, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Università degli Studi di Modena e Reggio Emilia, Systèmes Classiques ou Quantiques en Interaction, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, topology, time reversal, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Dimension (graph theory), FOS: Physical sciences, General Physics and Astronomy, Duality (optimization), 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, FOS: Mathematics, transport theory, Statistical physics, 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical Physics, Topology (chemistry), Mathematics, Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Probability (math.PR), Transport theory, Mathematical Physics (math-ph), free energy, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], lcsh:QC1-999, Transformation (function), High Energy Physics - Theory (hep-th), duality, Mathematics - Probability, lcsh:Physics
Abstract: A large family of diffusive models of transport that has been considered in the past years admits a transformation into the same model in contact with an equilibrium bath. This mapping holds at the full dynamical level, and is independent of dimension or topology. It provides a good opportunity to discuss questions of time reversal in out of equilibrium contexts. In particular, thanks to the mapping one may define the free-energy in the non-equilibrium states very naturally as the (usual) free energy of the mapped system., 20 pages, 1 figure
Published: 2020
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30. The Topological Symmetric Orbifold

Author: Songyuan Li, Jan Troost, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, Structure constants, FOS: Physical sciences, AdS-CFT Correspondence, Topology, 01 natural sciences, topological, symbols.namesake, algebra: Frobenius, Symmetric group, 0103 physical sciences, Frobenius algebra, surface, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, correlation function, 0101 mathematics, chiral ring, Orbifold, Physics, field theory: conformal, Conformal Field Theory, AdS/CFT correspondence, 010308 nuclear & particles physics, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010102 general mathematics, Cohomology, High Energy Physics - Theory (hep-th), Hilbert scheme, Conformal Field Models in String Theory, Topological Field Theories, symbols, cohomology, orbifold, lcsh:QC770-798
Abstract: We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by Hurwitz numbers. This proves a conjecture in the physics literature on extremal correlators. Moreover, it allows to leverage results on the combinatorics of the symmetric group to compute more structure constants explicitly. We recall that the full orbifold chiral ring is given by a symmetric orbifold Frobenius algebra. This construction enables the computation of topological genus zero and genus one correlators, and to prove the vanishing of higher genus contributions. The efficient description of all topological correlators sets the stage for a proof of a topological AdS/CFT correspondence. Indeed, we propose a concrete mathematical incarnation of the proof, relating Gromow-Witten theory in the bulk to the quantum cohomology of the Hilbert scheme on the boundary., 33 pages. v2: Remarks on proof added
Published: 2020
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31. Twisted String Theory in Anti-de Sitter Space

Author: Songyuan Li, Jan Troost, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, dimension: 3, Boundary (topology), string: twist, FOS: Physical sciences, AdS-CFT Correspondence, String theory, 01 natural sciences, String (physics), topological, space-time: anti-de Sitter, 0103 physical sciences, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, Tensor, string model, 010306 general physics, space: anti-de Sitter, Mathematical physics, Physics, 010308 nuclear & particles physics, Extended Supersymmetry, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Operator (physics), R symmetry, operator: vertex, U(1), AdS/CFT correspondence, High Energy Physics - Theory (hep-th), quantum gravity, symmetry: conformal, Conformal Field Models in String Theory, Topological Field Theories, tensor: energy-momentum, Quantum gravity, lcsh:QC770-798, Anti-de Sitter space
Abstract: We construct a string theory in three-dimensional anti-de Sitter space-time that is independent of the boundary metric. It is a topologically twisted theory of quantum gravity. We study string theories with an asymptotic N=2 superconformal symmetry and demonstrate that, when the world sheet coupling to the space-time boundary metric undergoes a U(1) R-symmetry twist, the space-time boundary energy-momentum tensor becomes topological. As a by-product of our analysis, we obtain the world sheet vertex operator that codes the space-time energy-momentum for conformally flat boundary metrics., 23 pages
Published: 2020
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32. Origin of the Six-Gluon Amplitude in Planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> Supersymmetric Yang-Mills Theory

Author: Georgios Papathanasiou, Benjamin Basso, Lance J. Dixon, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), SLAC National Accelerator Laboratory (SLAC), Stanford University [Stanford], DESY - Theory Group (DESY - Theory Group), and DESY Theory Group
Subjects: [PHYS]Physics [physics], Coupling, Coupling constant, Physics, General Physics and Astronomy, Yang–Mills theory, String theory, 01 natural sciences, Scattering amplitude, High Energy Physics::Theory, Amplitude, 0103 physical sciences, Operator product expansion, Resummation, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Mathematical physics
Abstract: We study the maximally-helicity-violating six-gluon scattering amplitude in planar N=4 super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of “anomalous dimensions” that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon operator product expansion, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the lightlike limit of the octagon, namely, the four-point function of large-charge Bogomol’nyi–Prasad–Sommerfield (BPS) operators.
Published: 2020
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33. Lie Algebra Fermions

Author: Jan Troost, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Statistics and Probability, High Energy Physics - Theory, Pure mathematics, dimension: 4, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], General Physics and Astronomy, FOS: Physical sciences, algebra: Lie, 01 natural sciences, gauge field theory: supersymmetry, 0103 physical sciences, Lie algebra, Supersymmetric quantum mechanics, Morse theory, 0101 mathematics, chiral ring, dimension: 2, Eigenvalues and eigenvectors, Mathematical Physics, Mathematics, Ring (mathematics), quantum mechanics: supersymmetry, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010102 general mathematics, Subalgebra, Lie algebra cohomology, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Cohomology, abelian, fermion number, High Energy Physics - Theory (hep-th), Modeling and Simulation, Spectral sequence, spectral, cohomology
Abstract: We define a supersymmetric quantum mechanics of fermions that take values in a simple Lie algebra. We summarize what is known about the spectrum and eigenspaces of the Laplacian which corresponds to the Koszul differential d. Firstly, we concentrate on the zero eigenvalue eigenspace which coincides with the Lie algebra cohomology. We provide physical insight into useful tools to compute the cohomology, namely Morse theory and the Hochschild-Serre spectral sequence. We list explicit generators for the Lie algebra cohomology ring. Secondly, we concentrate on the eigenspaces of the supersymmetric quantum mechanics with maximal eigenvalue at given fermion number. These eigenspaces have an explicit description in terms of abelian ideals of a Borel subalgebra of the simple Lie algebra. We also introduce a model of Lie algebra valued fermions in two dimensions, where the spaces of maximal eigenvalue acquire a cohomological interpretation. Our work provides physical interpretations of results by mathematicians, and simplifies the proof of a few theorems. Moreover, we recall that these mathematical results play a role in pure supersymmetric gauge theory in four dimensions, and observe that they give rise to a canonical representation of the four-dimensional chiral ring., 48 pages
Published: 2020
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34. Pure and twisted holography

Author: Jan Troost, Songyuan Li, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, dimension: 3, solution: quantization, FOS: Physical sciences, Duality (optimization), Boundary (topology), supersymmetry: 2, Liouville, boundary condition: twist, Conformal and W Symmetry, Space (mathematics), 01 natural sciences, Gauge-gravity correspondence, High Energy Physics::Theory, Theoretical physics, 0103 physical sciences, unitarity, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, Boundary value problem, chiral ring, dimension: 2, space: anti-de Sitter, 010306 general physics, field theory: conformal, Physics, AdS/CFT correspondence, Extended Supersymmetry, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Conformal field theory, Supergravity, High Energy Physics::Phenomenology, duality: holography, twist: topological, chiral, High Energy Physics - Theory (hep-th), quantum gravity, Topological Field Theories, lcsh:QC770-798, Quantum gravity, supergravity, Dual pair
Abstract: We analyse a simple example of a holographically dual pair in which we topologically twist both theories. The holography is based on the two-dimensional N=2 supersymmetric Liouville conformal field theory that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity theory in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configurations in the bulk supergravity theory and by quantising the solution space. Moreover, we note that the boundary calculation of the structure constants of the chiral ring carries over to the bulk theory as well. We thus construct a topological AdS/CFT duality in which the bulk theory is independent of the boundary metric., Comment: 21 pages
Published: 2020
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35. Lax matrices from antidominantly shifted Yangians and quantum affine algebras

Author: Frassek, Rouven, Pestun, Vasily, Tsymbaliuk, Alexander, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut des Hautes Etudes Scientifiques (IHES), IHES, Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Mathematics::Representation Theory
Abstract: We construct a family of $GL_n$ rational and trigonometric Lax matrices $T_D(z)$ parametrized by $\Lambda^+$-valued divisors $D$ on $\mathbb{P}^1$. To this end, we study the shifted Drinfeld Yangians $Y_\mu(\mathfrak{gl}_n)$ and quantum affine algebras $U_{\mu^+,\mu^-}(L\mathfrak{gl}_n)$, which slightly generalize their $\mathfrak{sl}_n$-counterparts of arxiv:1604.03625, arxiv:1708.01795. Our key observation is that both algebras admit the RTT type realization when $\mu$ (respectively, $\mu^+$ and $\mu^-$) are antidominant coweights. We prove that $T_D(z)$ are polynomial in $z$ (up to a rational factor) and obtain explicit simple formulas for those linear in $z$. This generalizes the recent construction by the first two authors of linear rational Lax matrices arxiv:1808.00799 in both trigonometric and higher $z$-degree directions. Furthermore, we show that all $T_D(z)$ are normalized limits of those parametrized by $D$ supported away of $\{\infty\}$ (in the rational case) or $\{0,\infty\}$ (in the trigonometric case). The RTT approach provides conceptual and elementary proofs for the construction of the coproduct homomorphisms on shifted Yangians and quantum affine algebras of $\mathfrak{sl}_n$, previously established via long computations in arxiv:1608.03331, arxiv:1708.01795. Finally, we establish a close relation between a certain collection of explicit linear Lax matrices and the well-known parabolic Gelfand-Tsetlin formulas.
Published: 2020

36. The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM

Author: Basso, Benjamin, Dixon, Lance J., Papathanasiou, Georgios, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), SLAC National Accelerator Laboratory (SLAC), Stanford University, Theory group, DESY (DESY), DESY ZEUTHEN, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS (LPTENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], scattering amplitude, scaling, coupling constant, FOS: Physical sciences, weak coupling, operator product expansion, anomalous dimension, High Energy Physics::Theory, High Energy Physics - Theory (hep-th), resummation, BPS [operator], strong coupling, ddc:530, supersymmetry, string model, 4 [n-point function]
Abstract: We study the maximally-helicity-violating (MHV) six-gluon scattering amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of "anomalous dimensions" that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon OPE, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the light-like limit of the octagon, namely the four-point function of large-charge BPS operators., Comment: 10 pages, 3 figures. v2: one section moved to appendix, other clarifying remarks added, minor typo's fixed
Published: 2020
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37. Oscillator realisations associated to the D-type Yangian: Towards the operatorial Q-system of orthogonal spin chains

Author: Rouven Frassek, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, Pure mathematics, Rank (linear algebra), [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, algebra: Lie, integrability, 01 natural sciences, Computer Science::Digital Libraries, Yangian, Factorization, factorization, 0103 physical sciences, Lie algebra, oscillator, FOS: Mathematics, multiplicity, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, transfer matrix, operator: Lax, 0101 mathematics, Representation Theory (math.RT), Mathematical Physics, Spin-½, Physics, Yang-Baxter equation: R-matrix, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010102 general mathematics, Degenerate energy levels, Mathematical Physics (math-ph), operator: Baxter, Dynkin diagram, Nonlinear Sciences::Exactly Solvable and Integrable Systems, High Energy Physics - Theory (hep-th), Fundamental representation, lcsh:QC770-798, Mathematics - Representation Theory, spin: chain
Abstract: We present a family of novel Lax operators corresponding to representations of the RTT-realisation of the Yangian associated with $D$-type Lie algebras. These Lax operators are of oscillator type, i.e. one space of the operators is infinite-dimensional while the other is in the first fundamental representation of $\mathfrak{so}(2r)$. We use the isomorphism between the first fundamental representation of $D_3$ and the $\mathbf{6}$ of $A_3$, for which the degenerate oscillator type Lax matrices are known, to derive the Lax operators for $r=3$. The results are used to generalise the Lax matrices to arbitrary rank for representations corresponding to the extremal nodes of the simply laced Dynkin diagram of $D_r$. The multiplicity of independent solutions at each extremal node is given by the dimension of the fundamental representation. We further derive certain factorisation formulas among these solutions and build transfer matrices with oscillators in the auxiliary space from the introduced degenerate Lax matrices. Finally, we provide some evidence that the constructed transfer matrices are Baxter Q-operators for $\mathfrak{so}(2r)$ spin chains by verifying certain QQ-relations for $D_4$ at low lengths., 17 pages, 2 figures; v2: references added; v3: published version
Published: 2020
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38. Punctures and p-spin curves from matrix models II

Author: Edouard Brézin, Shinobu Hikami, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, Pure mathematics, Logarithm, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, 01 natural sciences, Matrix model, String equation, symbols.namesake, constraint: Virasoro, 0103 physical sciences, correlation function, 0101 mathematics, spin: 1/2, spin: 3/2, Mathematical Physics, Mathematics, Spins, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Riemann surface, 010102 general mathematics, Statistical and Nonlinear Physics, Supersymmetry, matrix model: random, Mathematical Physics (math-ph), High Energy Physics - Theory (hep-th), string, symbols, supersymmetry, Random matrix, Ramond
Abstract: We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for p=1/2 and p=3/2. In those new cases one finds contributions from the Ramond sector, which were not present for positive integer p.The existence of Virasoro constraints, in particular a string equation, is considered also for half-integral spins. The contribution of the boundary of a Riemann surface, is investigated through a logarithmic matrix model The supersymmetric random matrices provide extensions to mixed positive and negative p punctures., Comment: 27 pages
Published: 2020
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39. N=4 SYM Quantum Spectral Curve in BFKL regime

Author: Alfimov, Mikhail, Gromov, Nikolay, Kazakov, Vladimir, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, AdS/CFT correspondence, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], High Energy Physics::Phenomenology, Baxter equation, Regge, FOS: Physical sciences, nonperturbative, integrability, expansion 1/N: color, anomalous dimension, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), supersymmetry: 4, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], numerical calculations
Abstract: We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N=4 supersymmetric Yang-Mills theory. QSC, based on quantum integrability of the AdS$_5$/CFT$_4$ duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N=4 SYM in the planar, $N_c\to\infty$ limit. We explain how to apply the QSC for the BFKL limit, which requires non-trivial analytic continuation in spin $S$ and extends the initial construction to non-local light-ray operators. We give a brief review of high precision non-perturbative numerical solutions and analytic perturbative data resulting from this approach. We also describe as a simple example of the QSC construction the leading order in the BFKL limit. We show that the QSC substantially simplifies in this limit and reduces to the Faddeev-Korchemsky Baxter equation for Q-functions. Finally, we review recent results for the Fishnet CFT, which carries a number of similarities with the Lipatov's integrable spin chain for interacting reggeized gluons., Comment: Contribution to the memorial volume "From the past to the future - the legacy of Lev Lipatov", 28 pages, 7 figures; v2: references added, typos fixed
Published: 2020
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40. Small-time expansion of the Fokker–Planck kernel for space and time dependent diffusion and drift coefficients

Author: Adel Bilal, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: High Energy Physics - Theory, FOS: Physical sciences, 01 natural sciences, 0103 physical sciences, any-dimensional, 0101 mathematics, Diffusion (business), Condensed Matter - Statistical Mechanics, Mathematical Physics, Heat kernel, Physics, asymptotic expansion, Statistical Mechanics (cond-mat.stat-mech), Spacetime, Fokker-Planck equation: solution, 010102 general mathematics, Mathematical analysis, diffusion, higher-order: 2, higher-order: 1, Statistical and Nonlinear Physics, Riemannian manifold, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), Kernel (image processing), Fokker–Planck equation, 010307 mathematical physics, Asymptotic expansion, Laplace operator
Abstract: We study the general solution of the Fokker-Planck equation in d dimensions with arbitrary space and time dependent diffusion matrix and drift term. We show how to construct the solution, for arbitrary initial distributions, as an asymptotic expansion for small time. This generalizes the well-known asymptotic expansion of the heat-kernel for the Laplace operator on a general Riemannian manifold. We explicitly work out the general solution to leading and next-to-leading order in this small-time expansion, as well as to next-to-next-to-leading order for vanishing drift. We illustrate our results on a several examples., Comment: 30 pages
Published: 2020
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41. Published for SISSA by Springer Analytic functional bootstrap for CFTs in d > 1

Author: Paulos, Miguel, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: [PHYS]Physics [physics], Conformal Field Theory, AdS-CFT Correspondence
Abstract: International audience; We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE, (double) lightcone and Regge limits. Compatibility with the crossing equation imposes constraints on the functional kernels which we study in detail. We then introduce two simple classes of func-tionals. The first class has a simple action on generalized free fields and their deformations and can be used to bootstrap AdS contact interactions in general dimension. The second class is obtained by tensoring holomorphic and antiholomorphic copies of d = 1 function-als which have been considered recently. They are dual to simple solutions to crossing in d = 2 which include the energy correlator of the Ising model. We show how these func-tionals lead to optimal bounds on the OPE density of d = 2 CFTs and argue that they provide an equivalent rewriting of the d = 2 crossing equation which is better suited for numeric computations than current approaches.
Published: 2020
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42. Spectral action in matrix form

Author: Ali H. Chamseddine, J. Iliopoulos, Walter D. van Suijlekom, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, dimension: 4, Physics and Astronomy (miscellaneous), FOS: Physical sciences, Gamma matrices, lcsh:Astrophysics, 01 natural sciences, symmetry: algebra, space: Euclidean, Theoretical physics, High Energy Physics - Phenomenology (hep-ph), 0103 physical sciences, Euclidean geometry, lcsh:QB460-466, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, structure, action: spectral, Matrix form, 010306 general physics, Engineering (miscellaneous), noncommutative, Mathematical Physics, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Electroweak interaction, Propagator, Noncommutative geometry, electroweak interaction: model, Formalism (philosophy of mathematics), High Energy Physics - Phenomenology, High Energy Physics - Theory (hep-th), gauge field theory: Yang-Mills, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], lcsh:QC770-798, propagator, quantization, Mathematics
Abstract: Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang-Mills theory. We illustrate the procedure for the toy electroweak model., 16 pages, 2 figures, changed equation numbering
Published: 2020
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43. Distributions in CFT. Part I. Cross-ratio space

Author: Slava Rychkov, Jiaxin Qiao, Petr Kravchuk, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut des Hautes Etudes Scientifiques (IHES), IHES, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Nuclear and High Energy Physics, dispersion relation, conformal block, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Boundary (topology), Conformal map, Field Theories in Higher Dimensions, Space (mathematics), Conformal and W Symmetry, 01 natural sciences, Correlation function, 0103 physical sciences, Convergence (routing), lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, correlation function, 010306 general physics, Physics, field theory: conformal, Conformal Field Theory, Series (mathematics), 010308 nuclear & particles physics, Conformal field theory, symmetry: crossing, Field Theories in Lower Dimensions, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Crossing, Mathematical analysis, lcsh:QC770-798, n-point function: 4
Abstract: International audience; We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of distributions on this boundary, i.e. it can be integrated term by term against appropriate test functions. This can be interpreted as a giving a new class of functionals that satisfy the swapping property when applied to the crossing equation, and we comment on the relation of our construction to other types of functionals. Our language is useful in all considerations involving the boundary of the region of convergence, e.g. for deriving the dispersion relations. We establish our results by elementary methods, relying only on crossing symmetry and the standard convergence properties of the conformal block expansion. This is the first in a series of papers on distributional properties of correlation functions in conformal field theory.
Published: 2020
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44. Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders

Author: B. Page, E. Pascual, Samuel Abreu, V. Sotnikov, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Nuclear and High Energy Physics, Particle physics, Photon, Hadron, FOS: Physical sciences, 01 natural sciences, quantum chromodynamics: correction, phase space, High Energy Physics - Phenomenology (hep-ph), NLO Computations, 0103 physical sciences, unitarity, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, 010306 general physics, numerical calculations, Particle Physics - Phenomenology, helicity: amplitude analysis, Physics, Quantum chromodynamics, loop integral, Unitarity, 010308 nuclear & particles physics, hadron: colliding beams, Analytic continuation, hep-ph, stability, photon: multiple production, QCD Phenomenology, Loop integral, Small set, color, High Energy Physics - Phenomenology, Phase space, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], lcsh:QC770-798, master integral
Abstract: We compute the two-loop helicity amplitudes for the production of three photons at hadron colliders in QCD at leading-color. Using the two-loop numerical unitarity method coupled with analytic reconstruction techniques, we obtain the decomposition of the two-loop amplitudes in terms of master integrals in analytic form. These expressions are valid to all orders in the dimensional regulator. We use them to compute the two-loop finite remainders, which are given in a form that can be efficiently evaluated across the whole physical phase space. We further package these results in a public code which assembles the helicity-summed squared two-loop remainders, whose numerical stability across phase-space is demonstrated. This is the first time that a five-point two-loop process is publicly available for immediate phenomenological applications., Comment: Minor text changes, updated references, and a typo fix. Matches the published version
Published: 2020
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45. Weyl invariant Jacobi forms along Higgsing trees

Author: Amir-Kian Kashani-Poor, Zhihao Duan, David Jaramillo Duque, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Global Symmetries, High Energy Physics - Theory, dimension: 5, Nuclear and High Energy Physics, partition function, invariance: Weyl, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Topological Strings, Field Theories in Higher Dimensions, QC770-798, 01 natural sciences, String (physics), Theoretical physics, Mathematics - Algebraic Geometry, High Energy Physics::Theory, Nuclear and particle physics. Atomic energy. Radioactivity, 0103 physical sciences, string: topological, FOS: Mathematics, Gauge theory, Invariant (mathematics), 010306 general physics, Algebraic Geometry (math.AG), compactification: circle, Gauge symmetry, field theory: conformal, Physics, Compactification (physics), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Partition function (mathematics), 16. Peace & justice, Symmetry (physics), High Energy Physics - Theory (hep-th), Gauge Symmetry, BPS, gauge field theory, Tree (set theory), spectrum: massless
Abstract: Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of Higgsing trees. We demonstrate that the specialization of the partition function as we move from the crown to the root of a tree is determined by homomorphisms between rings of Weyl invariant Jacobi forms. Our computations are made feasible by the fact that symmetry enhancements of the gauge theory which are manifest on the massless spectrum are inherited by the entire tower of BPS particles. In some cases, these symmetry enhancements have a nice relation to the 1-form symmetry of the associated gauge theory., Comment: 57 pages; v2 64 pages: discussion of specialization of Gromov-Witten invariants enhanced and moved to body of paper, with additional tables in appendix
Published: 2020
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46. Three-point functions at strong coupling in the BMN limit

Author: De-liang Zhong, Benjamin Basso, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, Nuclear and High Energy Physics, Structure constants, FOS: Physical sciences, field theory: string, 01 natural sciences, anomalous dimension, Planar, Operator (computer programming), 0103 physical sciences, strong coupling, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, Integrable Field Theories, 010306 general physics, Gamma function, space: anti-de Sitter, Mathematical physics, Physics, Field Theories in Higher Dimen- sions, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Supergravity, Magnon, String field theory, Supersymmetry, operator: primary, High Energy Physics - Theory (hep-th), Conformal Field Models in String Theory, supersymmetry: 4, lcsh:QC770-798, supergravity, n-point function: 3, magnon
Abstract: We consider structure constants of single-trace operators at strong coupling in planar $\mathcal{N}=4$ SYM theory using the hexagon formalism. We concentrate on heavy-heavy-light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex., 47 pages, 11 figures
Published: 2020
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47. Double-Scaling Limit in Principal Chiral Model: a New Non-Critical String?

Author: Vladimir Kazakov, Evgeny Sobko, Konstantin Zarembo, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Champs, Gravitation et Cordes, École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: High Energy Physics - Theory, FOS: Physical sciences, General Physics and Astronomy, nonperturbative, Computer Science::Digital Libraries, 01 natural sciences, Bethe ansatz, 0103 physical sciences, C++ string handling, string model, 010306 general physics, dimension: 2, Mathematical physics, Physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], hep-th, Principal (computer security), 16. Peace & justice, Scaling limit, Chiral model, High Energy Physics - Theory (hep-th), potential: chemical, Elementary Particles and Fields, expansion 1/N, SU(N) x SU(N), model: chiral, Particle Physics - Theory
Abstract: We initiate a systematic, non-perturbative study of the large-$N$ expansion in the two-dimensional $\text{SU}(N)\times \text{SU}(N)$ Principal Chiral Model (PCM). Starting with the known infinite-$N$ solution for the ground state at fixed chemical potential \cite{Fateev:1994dp,Fateev:1994ai}, we devise an iterative procedure to solve the Bethe ansatz equations order by order in $1/N$. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-$N$ expansion. The resulting double-scaling limit bears striking similarities to the $c=1$ non-critical string theory and suggests that the double-scaled PCM is dual to a non-critical string with a $(2+1)$-dimensional target space where an additional dimension emerges dynamically from the $\text{SU}(N)$ Dynkin diagram., 6 pages, 1 figure, v2: typos fixed, minor corrections
Published: 2019
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48. Thermodynamic Bethe Ansatz for Fishnet CFT

Author: Basso, Benjamin, Ferrando, Gwena��l, Kazakov, Vladimir, Zhong, De-liang, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Tel Aviv University [Tel Aviv], Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: High Energy Physics - Theory, [PHYS]Physics [physics], Nonlinear Sciences - Exactly Solvable and Integrable Systems, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], hep-th, math-ph, FOS: Physical sciences, Mathematical Physics (math-ph), High Energy Physics::Theory, math.MP, High Energy Physics - Theory (hep-th), Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics and Mathematics, nlin.SI, Mathematical Physics, Nonlinear Systems, Particle Physics - Theory
Abstract: We present the TBA equations and the Y-system for the exact spectrum of general multi-magnon local operators in the $D$-dimensional anisotropic version of the bi-scalar fishnet CFT. The mixing matrix of such operators is given in terms of fishnet planar graphs of multi-wheel and multi-spiral type. These graphs probe the two main building blocks of the TBA approach that are the magnon dispersion relation and the magnon scattering matrix and which we both obtain by diagonalising suitable graph-building operators. We also obtain the dual version of the TBA equations, which relates, in the continuum limit, $D$-dimensional graphs to two dimensional sigma models in $AdS_{D+1}$. It allows us to verify a general formula obtained by A.~Zamolodchikov for the critical coupling., 7 pages, 2 figures
Published: 2019

49. Introduction to Supersymmetry

Author: BILAL, ADEL, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
Abstract: 77 pages, no figures, Latex
Published: 2019

50. Introduction to Supersymmetry

Author: BILAL, ADEL, Champs, Gravitation et Cordes, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
Abstract: 77 pages, no figures, Latex
Published: 2019

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