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113 results on '"Jan Troost"'

1. Orbifolded elliptic genera of non-compact models

Author

Sujay K. Ashok and Jan Troost

Subjects
Conformal Field Models in String Theory, Conformal and W Symmetry, Sigma Models, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We revisit the flavored elliptic genus of the N=2 superconformal cigar model and generalize the analysis of the path integral result to the case of real central charge. It gives rise to a non-holomorphic modular covariant function generalizing completed mock modular forms. We also compute the genus for angular orbifolds of the cigar and Liouville theory and decompose it in terms of discrete and continuous contributions. The orbifolded elliptic genus at fractional level is a completed mock modular form with a shadow related to U(1) modular invariants at rational radius squared. We take the limit of the orbifolded genera towards a weighted ground state index and carefully interpret the contributions. We stress that the orbifold cigar and Liouville theories have a maximal and a minimal radius, respectively.

Published
2024
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2. The operator rings of topological symmetric orbifolds and their large N limit

Author

Sujay K. Ashok and Jan Troost

Subjects
1/N Expansion, Topological Field Theories, AdS-CFT Correspondence, Conformal Field Models in String Theory, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We compute the structure constants of topological symmetric orbifold theories up to third order in the large N expansion. The leading order structure constants are dominated by topological metric contractions. The first order interactions are single cycles joining while at second order we can have double joining as well as splitting. At third order, single cycle joining obtains genus one contributions. We also compute illustrative small N structure constants. Our analysis applies to all second quantized Frobenius algebras, a large class of algebras that includes the cohomology ring of the Hilbert scheme of points on K3 among many others. We point out interesting open questions that our results raise.

Published
2024
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3. More on pure gravity with a negative cosmological constant

Author

Lior Benizri and Jan Troost

Subjects
AdS-CFT Correspondence, Conformal and W Symmetry, Models of Quantum Gravity, Chern-Simons Theories, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We identify an ambiguity in the Chern-Simons formulation of three-dimensional gravity with negative cosmological constant that originates in an outer automorphism of the Lie algebra sl $$ \mathfrak{sl} $$ (2, ℝ). It has important consequences for the stability of the theory in a space-time with boundary. We revisit the classical equivalence of three-dimensional gravity with a boundary Liouville theory both on and off the mass shell. Moreover, we provide further details on the quantum equivalence, the gauge symmetry that renders the spectrum diagonal, as well as the relation between asymptotically AdS3 metrics and polar boundary conditions. We thus set the proposal that the Liouville conformal field theory serves as a definition of a unitary theory of pure gravity in three dimensions with negative cosmological constant on a more stable footing.

Published
2023
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4. The chiral ring of a symmetric orbifold and its large N limit

Author

Sujay K. Ashok and Jan Troost

Subjects
Conformal Field Models in String Theory, Topological Field Theories, 1/N Expansion, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We analyze the chiral operator ring of the symmetric orbifold conformal field theory on the complex two-plane ℂ2. We compute the large N limit of the ring and exhibit its factorized leading order behaviour. We moreover calculate all structure constants at the subleading and sub-subleading order. These features are coded as properties of the symmetric group and we review the relevant mathematical theorems on the product of conjugacy classes in the center of the group algebra. We illustrate the efficiency of the formalism by iteratively computing broad classes of higher point extremal correlators. We point out generalizations of our simplest of models and argue that our combinatorial analysis is relevant to the organization of the large N perturbation theory of generic symmetric orbifolds.

Published
2023
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5. Twisted strings in three-dimensional black holes

Author

Sujay K. Ashok and Jan Troost

Subjects
Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We revisit the classical dynamics of fundamental strings in BTZ black holes with NSNS flux. We analyze probe strings in the black hole background and determine their classical energy using a Nambu–Goto action. Three-dimensional gravity has a non-local effect on the metric surrounding a massive object which can be measured by winding strings. We also study the behaviour of short and long strings in the Wess–Zumino–Witten orbifold and show that their energy matches the long string probe analysis. In the process, we fix subtleties in the Lorentzian choice of NSNS flux. In Euclidean signature, we analyze the one-loop fundamental string partition function on the BTZ black hole and interpret the off-shell degrees of freedom as those of a coset orbifold. Finally, we speculate on how to identify the quantum Lorentzian string spectrum from the Euclidean orbifold partition function.

Published
2022
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6. Long strings and quasinormal winding modes

Author

Sujay K. Ashok and Jan Troost

Subjects
Conformal Field Models in String Theory, AdS-CFT Correspondence, Black Holes in String Theory, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We compute the path integral for a particle on the covering group of SL(2, ℝ) using a decomposition of the Lie algebra into adjoint orbits. We thus intuitively derive the Hilbert space of the particle on the group including discrete and continuous representations. Next, we perform a Lorentzian hyperbolic orbifold of the partition function and relate it to the Euclidean BTZ partition function. We use the particle model to inform further discussion of the spectral content of the one loop vacuum amplitude for strings on BTZ black hole backgrounds. We argue that the poles in the loop integrand code contributions of long string modes that wind the black hole. We moreover identify saddle point contributions of quasinormal winding modes.

Published
2022
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7. Topological two-dimensional gravity on surfaces with boundary

Author

Jan Troost

Subjects
Physics, QC1-999
Abstract

We solve two-dimensional gravity on surfaces with boundary in terms of contact interactions and surface degenerations. The known solution of the bulk theory in terms of a contact algebra is generalized to include boundaries and an enlarged set of boundary operators. The latter allow for a linearization of the Virasoro constraints in terms of an extended integrable KdV hierarchy.

Published
2023
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8. The AdS 3 × S 1 chiral ring

Author

Sujay K. Ashok, Songyuan Li, and Jan Troost

Subjects
Conformal Field Models in String Theory, AdS-CFT Correspondence, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We study AdS 3 × S 1 × Y supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 2 superconformal theory on Y.

Published
2021
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9. String scale thermal anti-de Sitter spaces

Author

Sujay K. Ashok and Jan Troost

Subjects
Conformal Field Models in String Theory, AdS-CFT Correspondence, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We study finite temperature string scale AdS 3 backgrounds. One background is AdS 3 × S 1 × T 2 in which the anti-de Sitter space-time and the circle are at the radius α ′ $$ \sqrt{\alpha^{\prime }} $$ . 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 × S 1 at curvature radius 2 α ′ / 3 $$ \sqrt{2{\alpha}^{\prime }/3} $$ . 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.

Published
2021
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10. Superstrings in thermal anti-de Sitter space

Author

Sujay K. Ashok and Jan Troost

Subjects
Conformal Field Models in String Theory, AdS-CFT Correspondence, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

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.

Published
2021
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11. Twisted string theory in anti-de Sitter space

Author

Songyuan Li and Jan Troost

Subjects
Conformal Field Models in String Theory, AdS-CFT Correspondence, Topological Field Theories, Extended Supersymmetry, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

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.

Published
2020
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12. The topological symmetric orbifold

Author

Songyuan Li and Jan Troost

Subjects
Conformal Field Models in String Theory, Topological Field Theories, AdS-CFT Correspondence, Conformal Field Theory, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We analyze 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 cohomology of the Hilbert scheme on the boundary.

Published
2020
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13. Pure and twisted holography

Author

Songyuan Li and Jan Troost

Subjects
Conformal and W Symmetry, Gauge-gravity correspondence, Topological Field Theories, Extended Supersymmetry, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We analyze 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 quantizing 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.

Published
2020
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14. Topological open/closed string dualities: matrix models and wave functions

Author

Sujay K. Ashok and Jan Troost

Subjects
D-branes, Integrable Hierarchies, Matrix Models, 2D Gravity, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalized Kontsevich matrix model in the large dimension limit. We integrate out off-diagonal degrees of freedom associated to one source eigenvalue, and find an open/closed topological string partition function, thus proving open/closed duality. We match the resulting open partition function to the generating function of intersection numbers on moduli spaces of Riemann surfaces with boundaries and boundary insertions. Moreover, we connect our work to the literature on a wave function of the KP integrable hierarchy and clarify the role of the extended Virasoro generators that include all time variables as well as the coupling to the open string observable.

Published
2019
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15. A duality in two-dimensional gravity

Author

Sujay K. Ashok and Jan Troost

Subjects
2D Gravity, Conformal Field Models in String Theory, Integrable Field Theories, Topological Field Theories, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We demonstrate an equivalence between two integrable flows defined in a polynomial ring quotiented by an ideal generated by a polynomial. This duality of integrable systems allows us to systematically exploit the Korteweg-de Vries hierarchy and its tau-function to propose amplitudes for non-compact topological gravity on Riemann surfaces of arbitrary genus. We thus quantize topological gravity coupled to non-compact topologica matter and demonstrate that this phase of topological gravity at N = 2 matter central charge larger than three is equivalent to the phase with matter of central charge smaller than three.

Published
2019
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16. Topological gravity with non-compact matter

Author

Songyuan Li and Jan Troost

Subjects
2D Gravity, Integrable Hierarchies, Topological Field Theories, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We couple twisted non-compact N = (2, 2) supersymmetric models to topological gravity in two dimensions. We propose expressions for the genus zero correlation functions based on a Kadomtsev-Petviashvili integrable hierarchy. Moreover, we prove recursion relations satisfied by the topological gravity amplitudes at all genera and compute characteristic critical exponents. We discuss the extent to which moving beyond the N = 2 central charge barrier opens a window on two-dimensional gravity with central charge larger than one.

Published
2019
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17. Liouville quantum gravity

Author

Songyuan Li, Nicolaos Toumbas, and Jan Troost

Subjects
Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological constant has peculiar properties. The quantum theory has no normalizable AdS3 vacuum. The model contains primary black holes with zero spin. All states can be interpreted as BTZ geometries dressed with boundary gravitons. There is a unique universal interaction between these states consistent with unitarity and the conformal symmetry of the model. This theory of gravity, though conceptually isolated from other models of quantum gravity, is worth scrutinizing.

Published
2020
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18. Twisted massive non-compact models

Author

Songyuan Li and Jan Troost

Subjects
Conformal Field Theory, Topological Field Theories, Conformal Field Models in String Theory, Extended Supersymmetry, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We study interacting massive N = (2, 2) supersymmetric field theories in two dimensions which arise from deforming conformal field theories with a continuous spectrum. Firstly, we deform N = 2 superconformal Liouville theory with relevant operators, and twist the theory into a topological quantum field theory. These theories can be thought of as twisted generalized Landau-Ginzburg models with negative power superpotential. We determine the structure constants of the chiral ring and therefore all correlators of these topological quantum field theories. We provide general formulas for the deformed operators of given charge as well as explicit solutions to the WDVV equations. Secondly, we analyze the topological anti-topological sector of the theory. We compute the metric at the conformal point through localization. Moreover, we show that the topological-anti-topological fusion differential equations on the metric in a family of non-compact theories takes the affine Toda form. The metric as a function of the family of theories is identical to the metric in certain deformed compact models. For a negative cubic power superpotential, for instance, it is governed by the Painlevé III differential equation.

Published
2018
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19. The conformal characters

Author

Antoine Bourget and Jan Troost

Subjects
Conformal and W Symmetry, Conformal Field Theory, Supersymmetry and Duality, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules. The Kazhdan-Lusztig polynomials code the relation between the Verma modules and the irreducible modules in the category and are the key to the characters of the conformal multiplets (whether finite dimensional, infinite dimensional, unitary or non-unitary). We discuss the representation theory and review in full generality which representations are unitarizable. The mathematical theory that allows for both the general treatment of characters and the full analysis of unitarity is made accessible. A good understanding of the mathematics of conformal multiplets renders the treatment of all highest weight representations in any dimension uniform, and provides an overarching comprehension of case-by-case results. Unitary highest weight representations and their characters are classified and computed in terms of data associated to cosets of the Weyl group of the conformal algebra. An executive summary is provided, as well as look-up tables up to and including rank four.

Published
2018
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20. An elliptic triptych

Author

Jan Troost

Subjects
Conformal Field Models in String Theory, Conformal Field Theory, Supersymmetry and Duality, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We clarify three aspects of non-compact elliptic genera. Firstly, we give a path integral derivation of the elliptic genus of the cigar conformal field theory from its non-linear sigma-model description. The result is a manifestly modular sum over a lattice. Secondly, we discuss supersymmetric quantum mechanics with a continuous spectrum. We regulate the theory and analyze the dependence on the temperature of the trace weighted by the fermion number. The dependence is dictated by the regulator. From a detailed analysis of the dependence on the infrared boundary conditions, we argue that in noncompact elliptic genera right-moving supersymmetry combined with modular covariance is anomalous. Thirdly, we further clarify the relation between the flat space elliptic genus and the infinite level limit of the cigar elliptic genus.

Published
2017
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21. Permutations of massive vacua

Author

Antoine Bourget and Jan Troost

Subjects
Supersymmetric Gauge Theory, Supersymmetry and Duality, Gauge Symmetry, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N $$ \mathcal{N} $$ = 1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N $$ \mathcal{N} $$ = 4 and N $$ \mathcal{N} $$ = 2 theories with N $$ \mathcal{N} $$ = 1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.

Published
2017
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22. On the gl(1|1) Wess-Zumino-Witten model

Author

Jan Troost

Subjects
Conformal Field Models in String Theory, Conformal Field Theory, AdS-CFT Correspondence, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract We continue the study of the gl(1|1) Wess-Zumino-Witten model. The Knizhnik-Zamolodchikov equations for the one, two, three and four point functions are analyzed, for vertex operators corresponding to typical and projective representations. We demonstrate their interplay with the logarithmic global conformal Ward identities. We compute the four point function for one projective and three typical representations. Three coupled first order Knizhnik-Zamolodchikov equations are integrated consecutively in terms of generalized hypergeometric functions, and we assemble the solutions into a local correlator. Moreover, we prove crossing symmetry of the four point function of four typical representations at generic momenta. Throughout, the map between the gl(1|1) Wess-Zumino-Witten model and symplectic fermions is exploited and extended.

Published
2017
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23. Path Integrals on sl(2,R) Orbits

Author

Sujay K Ashok and Jan Troost

Subjects
Statistics and Probability, High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Modeling and Simulation, General Physics and Astronomy, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics
Abstract

We quantise orbits of the adjoint group action on elements of the sl(2,R) Lie algebra. The path integration along elliptic slices is akin to the coadjoint orbit quantization of compact Lie groups, and the calculation of the characters of elliptic group elements proceeds along the same lines as in compact groups. The computation of the trace of hyperbolic group elements in a diagonal basis as well as the calculation of the full group action on a hyperbolic basis requires considerably more technique. We determine the action of hyperbolic one-parameter subgroups of PSL(2,R) on the adjoint orbits and discuss global subtleties in choices of adapted coordinate systems. Using the hyperbolic slicing of orbits, we describe the quantum mechanics of an irreducible sl(2,R) representation in a hyperbolic basis and relate the basis to the mathematics of the Mellin integral transform. We moreover discuss the representation theory of the double cover SL(2,R) of PSL(2,R) as well as that of its universal cover. Traces in the representations of these groups for both elliptic and hyperbolic elements are computed. Finally, we motivate our treatment of this elementary quantisation problem by indicating applications., 38 pages, 6 figures

Published
2022

24. 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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25. 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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26. 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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27. 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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28. Topological Open/Closed String Dualities: Matrix Models and Wave Functions

Author

Jan Troost, Sujay K. Ashok, 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), Institute of Mathematical Sciences [Chennai] (IMSc), 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, Nuclear and High Energy Physics, wave function, Boundary (topology), Duality (optimization), FOS: Physical sciences, Topology, 01 natural sciences, String (physics), string: open, symbols.namesake, 0103 physical sciences, string: topological, string: closed, integrability: hierarchy, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, gravitation: coupling, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Generating function (physics), Physics, Matrix Models, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Riemann surface, Integrable Hierarchies, matrix model, duality: string, Function (mathematics), Partition function (mathematics), Moduli space, string: partition function, High Energy Physics - Theory (hep-th), D-branes, symbols, lcsh:QC770-798, moduli space, Virasoro, 2D Gravity, gravitation: topological
Abstract

We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalised Kontsevich matrix model in the large dimension limit. We integrate out off-diagonal degrees of freedom associated to one source eigenvalue, and find an open/closed topological string partition function, thus proving open/closed duality. We match the resulting open partition function to the generating function of intersection numbers on moduli spaces of Riemann surfaces with boundaries and boundary insertions. Moreover, we connect our work to the literature on a wave function of the KP integrable hierarchy and clarify the role of the extended Virasoro generators that include all time variables as well as the coupling to the open string observable., Comment: 24 pages

Published
2019
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30. Liouville quantum gravity

Author

Jan Troost, Nicolaos Toumbas, Songyuan Li, 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), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de Physique Théorique de l'ENS (LPTENS), 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)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Nuclear and High Energy Physics, dimension: 3, spin: 0, FOS: Physical sciences, quantum gravity: model, Cosmological constant, cosmological constant: negative, Liouville, 01 natural sciences, Gravitation, High Energy Physics::Theory, General Relativity and Quantum Cosmology, Theoretical physics, Conformal symmetry, 0103 physical sciences, anti-de Sitter, black hole, unitarity, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, 010306 general physics, field theory: conformal, Physics, Unitarity, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Conformal field theory, Graviton, duality: holography, Black hole, High Energy Physics - Theory (hep-th), gravitation, symmetry: conformal, graviton, lcsh:QC770-798, Quantum gravity
Abstract

We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological constant has peculiar properties. The quantum theory has no normalisable AdS3 vacuum. The model contains primary black holes with zero spin. All states can be interpreted as black holes dressed with boundary gravitons. There is a unique universal interaction between these states consistent with unitarity and the conformal symmetry of the model. This theory of gravity, though conceptually isolated from other models of quantum gravity, is worth scrutinising., Comment: 26 pages, journal version

Published
2020
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31. Exact WKB analysis of N $$ \mathcal{N} $$ = 2 gauge theories

Author

Jan Troost, Madhusudhan Raman, Renjan R. John, Sujay K. Ashok, Dileep P. Jatkar, Institute of Mathematical Sciences [Chennai] (IMSc), 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Nuclear and High Energy Physics, Instanton, 010308 nuclear & particles physics, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Order (ring theory), 01 natural sciences, WKB approximation, Monodromy, Gauge group, Supersymmetric gauge theory, Quantum mechanics, 0103 physical sciences, Gauge theory, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Mathematical physics
Abstract

We study $ \mathcal{N} $ = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by ϵ$_{1}$- and ϵ$_{2}$-deformed instanton partition functions. We confirm their validity at leading order in ϵ$_{2}$ via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of ϵ$_{1}$-deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of ϵ$_{1}$ is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.

Published
2016
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32. The covariant chiral ring

Author

Jan Troost, Antoine Bourget, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Ring (mathematics), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, FOS: Physical sciences, Supersymmetry, Lorentz covariance, Space (mathematics), 01 natural sciences, String (physics), Moduli space, High Energy Physics - Theory (hep-th), 0103 physical sciences, Covariant transformation, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Orbifold, Mathematical physics
Abstract

We construct a covariant generating function for the spectrum of chiral primaries of symmetric orbifold conformal field theories with N=(4,4) supersymmetry in two dimensions. For seed target spaces K3 and T4, the generating functions capture the SO(21) and SO(5) representation theoretic content of the chiral ring respectively. Via string dualities, we relate the transformation properties of the chiral ring under these isometries of the moduli space to the Lorentz covariance of perturbative string partition functions in flat space., Comment: 19 pages

Published
2016
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33. On the N = 1 ∗ $$ \mathcal{N}={1}^{\ast } $$ gauge theory on a circle and elliptic integrable systems

Author

Jan Troost, Antoine Bourget, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Nuclear and High Energy Physics, Compactification (physics), 010308 nuclear & particles physics, Group (mathematics), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], High Energy Physics::Phenomenology, Nilpotent orbit, 01 natural sciences, Centralizer and normalizer, Nilpotent, High Energy Physics::Theory, Conjugacy class, Supersymmetric gauge theory, 0103 physical sciences, Gauge theory, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Mathematical physics
Abstract

We continue our study of the N = 1 ∗ $$ \mathcal{N}={1}^{\ast } $$ supersymmetric gauge theory on ℝ 2 , 1 × S 1 $$ {\mathbb{R}}^{2,1}\times {S}^1 $$ and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the classification of nilpotent orbits, as well as on the conjugacy classes of the component group of their centralizer. We demonstrate that semi-classically massless vacua can be lifted by Wilson lines in unbroken discrete gauge groups. The pseudo-Levi subalgebras that play a classifying role in the nilpotent orbit theory are also key in defining generalized Inozemtsev limits of (twisted) elliptic integrable systems. We illustrate our analysis in the N = 1 ∗ $$ \mathcal{N}={1}^{\ast } $$ theories with gauge algebras su (3), su (4), so (5) and for the exceptional gauge algebra G 2 . We map out modular duality diagrams of the massive and massless vacua. Moreover, we provide an analytic description of the branches of massless vacua in the case of the su (3) and the so (5) theory. The description of these branches in terms of the complexified Wilson lines on the circle invokes the Eichler-Zagier technique for inverting the elliptic Weierstrass function. After fine-tuning the coupling to elliptic points of order three, we identify the Argyres-Douglas singularities of the su (3) N = 1 ∗ $$ \mathcal{N}={1}^{\ast } $$ theory.

Published
2016
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34. Alternative procedure to shorten rectal barostat procedure for the assessment of rectal compliance and visceral perception: a feasibility study

Author

Robert-Jan M. Brummer, Daisy Jonkers, S.A.L.W. Vanhoutvin, Ad A.M. Masclee, Konraad Venema, Frederik Jan Troost, T. O. C. Kilkens, Patrick J. Lindsey, Interne Geneeskunde, Complexe Genetica, RS: NUTRIM - R2 - Gut-liver homeostasis, RS: CARIM School for Cardiovascular Diseases, and RS: GROW - School for Oncology and Reproduction

Subjects
Original Article—Alimentary Tract, Adult, Male, medicine.medical_specialty, Time Factors, genetic structures, Rectum, Distension, Irritable Bowel Syndrome, Clinical Protocols, Sensation, medicine, Visceral perception, Pressure, Humans, Rectal compliance, Irritable bowel syndrome, Pain Measurement, business.industry, digestive, oral, and skin physiology, Gastroenterology, Rectal capacity, Middle Aged, medicine.disease, Barostat, Dilatation, Colorectal surgery, Compliance (physiology), medicine.anatomical_structure, Anesthesia, Minimal distension pressure, Case-Control Studies, Physical therapy, Feasibility Studies, Female, Rectal, business, Gastrointestinal Motility, Abdominal surgery
Abstract

Background Barostat methodology is widely used for assessing visceral perception. Different barostat protocols are described with respect to the measurement of rectal compliance and visceral perception. The choice of protocols affects the duration, which is normally 60–90 min, and accuracy of the procedure. This study aimed to shorten the procedure by using the semi-random distension protocol for both compliance and visceral perception measurement and a correction based on rectal capacity (RC) instead of minimal distension pressure (MDP). Methods Twelve irritable bowel syndrome (IBS) patients (7 females) and 11 healthy controls (8 females) underwent a barostat procedure. Compliance was determined during both a staircase distension and a semi-random protocol. Visceral perception data were compared as a function of pressure or relative volume, corrected for MDP or RC, respectively. Results Compliance measurement using the semi-random protocol instead of the staircase distension protocol resulted in an overestimation in healthy volunteers, but not in IBS patients. The overall conclusion that IBS patients had a lower compliance compared to controls was not different between protocols. Data presentation of the visceral perception scores as a function of corrected volume instead of pressures corrected for MDP did not alter the conclusion that sensation scores in IBS patients were higher as compared to healthy controls. Conclusions This study showed that barostat procedures may be shortened by approximately 20 min, without losing the ability to discriminate between healthy controls and IBS patients. A correction for RC instead of MDP may improve the accuracy of the procedure. Electronic supplementary material The online version of this article (doi:10.1007/s00535-012-0543-x) contains supplementary material, which is available to authorized users.

Published
2012

35. The AdS3 boundary energy–momentum tensor, exact in the string length over the curvature radius

Author

Jan Troost

Subjects
Physics, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Worldsheet, Conformal field theory, Bosonic string theory, String field theory, String theory, 01 natural sciences, High Energy Physics::Theory, Non-critical string theory, Quantum mechanics, 0103 physical sciences, Virasoro algebra, String cosmology, 010306 general physics, Mathematical physics
Abstract

We clarify the map between boundary perturbations of AdS 3 in general relativity, and exactly marginal worldsheet vertex operators in AdS 3 string theory with Neveu–Schwarz Neveu–Schwarz flux. The latter correspond to solutions of the higher derivative low-energy tree level effective action to all orders in the string length over the curvature radius. We calculate the exact expression of the boundary energy–momentum tensor including all these higher derivative corrections in a purely bosonic string theory. The bottom-line is a canonical shift in the normalization of the boundary energy–momentum tensor corresponding to a shift in the curvature radius over the string length squared by the dual Coxeter number of the SL ( 2 , R ) subalgebra of the space–time Virasoro algebra. That allows us to propose a value for the Brown–Henneaux central charge including all tree level higher derivative corrections in bosonic string theory, in a scheme dictated by the worldsheet conformal field theory.

Published
2010
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36. Duality and modularity in elliptic integrable systems and vacua of N = 1 ∗ $$ \mathcal{N}={1}^{\ast } $$ gauge theories

Author

Jan Troost, Antoine Bourget, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Nuclear and High Energy Physics, Pure mathematics, Triality, Fundamental domain, Modular group, Supersymmetric gauge theory, Gauge group, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Modular form, Type (model theory), ComputingMilieux_MISCELLANEOUS, Congruence subgroup
Abstract

We study complexified elliptic Calogero-Moser integrable systems. We determine the value of the potential at isolated extrema, as a function of the modular parameter of the torus on which the integrable system lives. We calculate the extrema for low rank B,C,D root systems using a mix of analytical and numerical tools. For so(5) we find convincing evidence that the extrema constitute a vector valued modular form for the Γ0(4) congruence subgroup of the modular group. For so(7) and so(8), the extrema split into two sets. One set contains extrema that make up vector valued modular forms for congruence subgroups (namely Γ0(4), Γ(2) and Γ(3)), and a second set contains extrema that exhibit monodromies around points in the interior of the fundamental domain. The former set can be described analytically, while for the latter, we provide an analytic value for the point of monodromy for so(8), as well as extensive numerical predictions for the Fourier coefficients of the extrema. Our results on the extrema provide a rationale for integrality properties observed in integrable models, and embed these into the theory of vector valued modular forms. Moreover, using the data we gather on the modularity of complexified integrable system extrema, we analyse the massive vacua of mass deformed $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theories with low rank gauge group of type B, C and D. We map out their transformation properties under the infrared electric-magnetic duality group as well as under triality for $$ \mathcal{N}={1}^{\ast } $$ with gauge algebra so(8). We compare the exact massive vacua on $$ {\mathbb{R}}^3\times {S}^1 $$ to those found in a semi-classical analysis on $$ {\mathbb{R}}^4 $$ . We identify several intriguing features of the quantum gauge theories.

Published
2015
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37. D-branes in Liouville theory and its mirror

Author

Jan Troost, Dan Israel, and Ari Pakman

Subjects
Physics, Nuclear and High Energy Physics, Field (physics), 010308 nuclear & particles physics, Conformal field theory, Basis (universal algebra), 01 natural sciences, Spectral line, High Energy Physics::Theory, Quantum mechanics, 0103 physical sciences, Brane cosmology, Coset, Liouville field theory, 010306 general physics, Mathematics::Symplectic Geometry, Orbifold, Mathematical physics
Abstract

We study D-branes in the mirror pair N = 2 Liouville/supersymmetric SL ( 2 , R ) / U ( 1 ) coset superconformal field theories. We build D0-, D1- and D2-branes, on the basis of the boundary state construction for the H 3 + conformal field theory. We also construct D0-branes in an orbifold that rotates the angular direction of the cigar. We show how the poles of correlators associated to localized states and bulk interactions naturally decouple in the one-point functions of localized and extended branes. We stress the role played in the analysis of D-brane spectra by primaries in SL ( 2 , R ) / U ( 1 ) which are descendents of the parent theory.

Published
2005
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38. Quantum geometry from the toroidal block

Author

Jan Troost, Amir-Kian Kashani-Poor, Laboratoire de Physique Théorique de l'ENS (LPTENS), 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)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Quantum geometry, Toroid, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], FOS: Physical sciences, Conformal map, Decoupling (cosmology), Conformal dimension, Theoretical physics, High Energy Physics - Theory (hep-th), Null vector, Central charge, ComputingMilieux_MISCELLANEOUS
Abstract

We continue our study of the semi-classical (large central charge) expansion of the toroidal one-point conformal block in the context of the 2d/4d correspondence. We demonstrate that the Seiberg-Witten curve and (epsilon1-deformed) differential emerge naturally in conformal field theory when computing the block via null vector decoupling equations. This framework permits us to derive epsilon1-deformations of the conventional relations governing the prepotential. These enable us to complete the proof of the quasi-modularity of the coefficients of the conformal block in an expansion around large exchanged conformal dimension. We furthermore derive these relations from the semi-classics of exact conformal field theory quantities, such as braiding matrices and the S-move kernel. In the course of our study, we present a new proof of Matone's relation for N=2* theory., 27 pages, 1 figure

Published
2014
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39. Higher poles and crossing phenomena from twisted genera

Author

Jan Troost, Sujay K. Ashok, E. Dell'Aquila, Institute of Mathematical Sciences [Chennai] (IMSc), 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Angular momentum, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Conformal field theory, Worldsheet, FOS: Physical sciences, Supersymmetry, 01 natural sciences, symbols.namesake, High Energy Physics - Theory (hep-th), 0103 physical sciences, Bound state, symbols, Covariant transformation, Supersymmetric quantum mechanics, 010306 general physics, Hamiltonian (quantum mechanics), Mathematical physics
Abstract

We demonstrate that Appell-Lerch sums with higher order poles as well as their modular covariant completions arise as partition functions in the cigar conformal field theory with worldsheet supersymmetry. The modular covariant derivatives of the elliptic genus of the cigar give rise to operator insertions corresponding to (powers of) right-moving momentum, left-moving fermion number, as well as a term corresponding to an ordinary zero mode partition sum. To show this, we demonstrate how the right-moving supersymmetric quantum mechanics (and in particular the Hamiltonian and spectral density) depend on the imaginary part of the chemical potential for angular momentum. As a consequence of our analysis we find that varying the imaginary part of the chemical potential for angular momentum on the cigar gives rise to a wall-crossing phenomenon in the bound state contribution to the elliptic genus, while the full elliptic genus is a continuous function of the chemical potential., 29 pages

Published
2014
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40. Localization and real Jacobi forms

Author

Sujay K. Ashok, Jan Troost, Nima Doroud, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Asymptotically linear, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, High Energy Physics::Phenomenology, FOS: Physical sciences, Sigma, Supersymmetry, 01 natural sciences, High Energy Physics::Theory, High Energy Physics - Theory (hep-th), Flow (mathematics), 0103 physical sciences, Isometry, Dilaton, Abelian group, 010306 general physics, Mathematical physics
Abstract

We calculate the elliptic genus of two dimensional abelian gauged linear sigma models with (2,2) supersymmetry using supersymmetric localization. The matter sector contains charged chiral multiplets as well as Stueckelberg fields coupled to the vector multiplets. These models include theories that flow in the infrared to non-linear sigma models with target spaces that are non-compact Kahler manifolds with U(N) isometry and with an asymptotically linear dilaton direction. The elliptic genera are the modular completions of mock Jacobi forms that have been proposed recently using complementary arguments. We also compute the elliptic genera of models that contain multiple Stueckelberg fields from first principles., Comment: 19+1 pages, LaTeX. Minor correction

Published
2014
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41. Lessons on Black Holes from the Elliptic Genus

Author

Jan Troost, Amit Giveon, Nissan Itzhaki, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Continuum (topology), Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Holomorphic function, Holonomy, FOS: Physical sciences, String theory, Theoretical physics, High Energy Physics - Theory (hep-th), Genus (mathematics), Field theory (psychology), Schwarzschild radius
Abstract

We further study the elliptic genus of the cigar SL(2,R)/U(1) coset superconformal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and non-holomorphic parts that are due to the discrete states and a mismatch in the spectral densities of the continuum, respectively. The mismatch in the continuum is universal, in the sense that it is fully determined by the asymptotic cylindrical topology of the cigar's throat. Since modularity of the elliptic genus requires both the holomorphic and non-holomorphic parts, the holomorphic term is universal as well. The contribution of the discrete states is thus present even for perturbative strings propagating in the background of large Schwarzschild black holes. We argue that the discrete states live at a stringy distance from the tip of the cigar both from the conformal field theory wave-function analysis and from a holonomy space perspective. Thus, the way string theory takes care of its self-consistency seems to have important consequences for the physics near horizons, even for parametrically large black holes., Comment: 33 pages, 2 figures

Published
2014

42. Elliptic genera and real Jacobi forms

Author

Sujay K. Ashok, Jan Troost, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Pure mathematics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Infrared fixed point, Conformal field theory, Complex projective space, FOS: Physical sciences, 01 natural sciences, Jacobi form, Matrix (mathematics), High Energy Physics - Theory (hep-th), 0103 physical sciences, Isometry, Mock modular form, 010306 general physics, Central charge
Abstract

We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional N=(2,2) supersymmetric theories. They arise in a family labeled by two integers N and k which determine the central charge of the infrared fixed point through the formula c=3N(1+ 2N/k). We decompose the real Jacobi form into a mock modular form and a term arising from the continuous spectrum of the conformal field theory. We argue that the Jacobi form represents the elliptic genus of a theory defined on a 2N dimensional background with U(N) isometry, containing a complex projective space section, a circle fiber and a linear dilaton direction. We also present formulas for the elliptic genera of orbifolds of these models., Comment: 32 pages

Published
2014
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43. The algebra of diffeomorphisms from the world sheet

Author

Jan Troost, Waldemar Schulgin, Université libre de Bruxelles (ULB), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), 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), and 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)

Subjects
Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, Unitarity, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Bosonic Strings, Space-Time Symmetries, FOS: Physical sciences, Field (mathematics), 16. Peace & justice, String theory, Physique atomique et nucléaire, Algebra, Operator algebra, High Energy Physics - Theory (hep-th), Conformal Field Models in String Theory, Tensor (intrinsic definition), Vertex (curve), Diffeomorphism, BRST Symmetry
Abstract

The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras., SCOPUS: ar.j, info:eu-repo/semantics/published

Published
2014
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44. The longitudinal fivebrane and tachyon condensation in matrix theory

Author

Marc Massar, Jan Troost, 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), Physics, Theoretical Physics, Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, Tachyon condensation, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, Supergravity, FOS: Physical sciences, Theoretical elementary particle physics, Equations of motion, Charge (physics), 01 natural sciences, Action (physics), High Energy Physics - Theory (hep-th), Tachyon, 0103 physical sciences, Bound state, 010306 general physics, Mathematical physics
Abstract

We study a configuration in matrix theory carying longitudinal fivebrane charge, i.e. a D0-D4 bound state. We calculate the one-loop effective potential between a D0-D4 bound state and a D0-anti-D4 bound state and compare our results to a supergravity calculation. Next, we identify the tachyonic fluctuations in the D0-D4 and D0-anti-D4 system. We analyse classically the action for these tachyons and find solutions to the equations of motion corresponding to tachyon condensation., 19 pages

Published
2000
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45. Off-shell formulation of N = 2 non-linear σ-models

Author

Jan Troost, Alexander Sevrin, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, High Energy Physics::Lattice, High Energy Physics::Phenomenology, Shell (structure), FOS: Physical sciences, Sigma, Superfield, Superspace, 01 natural sciences, High Energy Physics::Theory, Nonlinear system, High Energy Physics - Theory (hep-th), 0103 physical sciences, 010306 general physics, Multiplet, Mathematical physics
Abstract

We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted chiral and semi-chiral ones. We study the resulting sigma-models and we speculate on the possibility that all (2,2) non-linear sigma-models can be described using these fields. We apply the results to two examples: the SU(2) x U(1) and the SU(2) x SU(2) WZW model. Pending upon the choice of complex structures, the former can be described in terms of either one semi-chiral multiplet or a chiral and a twisted chiral multiplet. The latter is formulated in terms of one semi-chiral and one twisted chiral multiplet. For both cases we obtain the potential explicitely., 22 pages, LaTeX

Published
1997
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46. The Black Hole Interior and a Curious Sum Rule

Author

Jan Troost, Amit Giveon, Nissan Itzhaki, The Hebrew University of Jerusalem (HUJ), Tel Aviv University [Tel Aviv], 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), Tel Aviv University (TAU), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, Worldsheet, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], FOS: Physical sciences, String theory, Minimal model, Black hole, Theoretical physics, General Relativity and Quantum Cosmology, High Energy Physics::Theory, Singularity, High Energy Physics - Theory (hep-th), Euclidean geometry, Black brane, Sum rule in quantum mechanics
Abstract

We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics., 8 pages, 2 figures

Published
2013

47. Transformations of Spherical Blocks

Author

Amir-Kian Kashani-Poor, Jan Troost, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, High Energy Physics - Theory, Weyl group, Instanton, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010102 general mathematics, FOS: Physical sciences, Decoupling (cosmology), Topological string theory, 01 natural sciences, symbols.namesake, High Energy Physics - Theory (hep-th), Null vector, 0103 physical sciences, symbols, Gauge theory, Affine transformation, 0101 mathematics, Mathematical physics
Abstract

We further explore the correspondence between N=2 supersymmetric SU(2) gauge theory with four flavors on epsilon-deformed backgrounds and conformal field theory, with an emphasis on the epsilon-expansion of the partition function natural from a topological string theory point of view. Solving an appropriate null vector decoupling equation in the semi-classical limit allows us to express the instanton partition function as a series in quasi-modular forms of the group Gamma(2), with the expected symmetry Weyl group of SO(8) semi-direct S_3. In the presence of an elementary surface operator, this symmetry is enhanced to an action of the affine Weyl group of SO(8) semi-direct S_4 on the instanton partition function, as we demonstrate via the link between the null vector decoupling equation and the quantum Painlev\'e VI equation., Comment: 31 pages, 1 figure; v2: typos corrected, references added

Published
2013
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48. Counting Strings, Wound and Bound

Author

Suresh Nampuri, Sujay K. Ashok, Jan Troost, Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), 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), and 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)

Subjects
Physics, Heterotic string theory, High Energy Physics - Theory, Nuclear and High Energy Physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, FOS: Physical sciences, 16. Peace & justice, Dirac operator, String theory, 01 natural sciences, String (physics), Domain wall (string theory), symbols.namesake, Theoretical physics, Counting problem, High Energy Physics - Theory (hep-th), 0103 physical sciences, Bound state, symbols, Dilaton, 010306 general physics
Abstract

We analyze zero mode counting problems for Dirac operators that find their origin in string theory backgrounds. A first class of quantum mechanical models for which we compute the number of ground states arises from a string winding an isometric direction in a geometry, taking into account its energy due to tension. Alternatively, the models arise from deforming marginal bound states of a string winding a circle, and moving in an orthogonal geometry. After deformation, the number of bound states is again counted by the zero modes of a Dirac operator. We count these bound states in even dimensional asymptotically linear dilaton backgrounds as well as in Euclidean Taub-NUT. We show multiple pole behavior in the fugacities keeping track of a U(1) charge. We also discuss a second class of counting problems that arises when these backgrounds are deformed via the application of a heterotic duality transformation. We discuss applications of our results to Appell-Lerch sums and the counting of domain wall bound states., 38 pages

Published
2013

49. Asymptotic symmetry groups and operator algebras

Author

Jan Troost, Waldemar Schulgin, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Physics, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Worldsheet, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], FOS: Physical sciences, Symmetry group, String theory, 01 natural sciences, String (physics), High Energy Physics::Theory, High Energy Physics - Theory (hep-th), 0103 physical sciences, Vertex (curve), Quantum gravity, Diffeomorphism, 010306 general physics, Mathematical physics
Abstract

We associate vertex operators to space-time diffeomorphisms in flat space string theory, and compute their algebra, which is a diffeomorphism algebra with higher derivative corrections. As an application, we realize the asymptotic symmetry group BMS3 of three-dimensional flat space in terms of vertex operators on the string worldsheet. This provides an embedding of the BMS3 algebra in a consistent theory of quantum gravity. Higher derivative corrections vanish asymptotically. An appendix is dedicated to alpha prime corrected algebras in conformal field theory and string theory., Comment: 25 pages

Published
2013
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50. The toroidal block and the genus expansion

Author

Jan Troost, Amir-Kian Kashani-Poor, 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), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, High Energy Physics - Theory, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], FOS: Physical sciences, Conformal map, Partition function (mathematics), 01 natural sciences, String (physics), Theoretical physics, High Energy Physics::Theory, High Energy Physics - Theory (hep-th), Genus (mathematics), 0103 physical sciences, Field theory (psychology), Gauge theory, Limit (mathematics), 010306 general physics
Abstract

We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via geometric engineering from the topological string. This point of view uncovers modular properties of the one-point conformal block on a torus with complexified intermediate momenta: in the large intermediate weight limit, it is a power series whose coefficients are quasi-modular forms. The all-genus viewpoint that the conformal field theory approach lends to the topological string yields insight into the analytic structure of the topological string partition function in the field theory limit., 36 pages

Published
2012
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