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The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some certain conditions. We have gone on to refine the classification of the potential function with respect to gradient h-almost conformal η-Ricci-Bourguignon soliton in a perfect uid spacetime with torse-forming vector field ξ. Finally, we have developed an example of h-almost conformal η-Ricci-Bourguignon soliton. [ABSTRACT FROM AUTHOR]

In a recent paper, Gorbenko and Zan [1] observed that O(n) symmetry alone does not protect the well-known renormalization group flow from the dilute to the dense phase of the two-dimensional O(n) model under thermal perturbations. We show in this paper that the required "extra protection" is topological in nature, and is related to the existence of certain non-invertible topological defect lines. We define these defect lines and discuss the ensuing topological protection, both in the context of the O(n) lattice model and in its recently understood continuum limit, which takes the form of a conformal field theory governed by an interchiral algebra. [ABSTRACT FROM AUTHOR]

In this paper, we studied the thermodynamic quantities of dyonic ModMax and Taub-NUT black holes (BHs) to investigate their universal relations, viz. that product formulas are mass-independent. So, we calculated the thermodynamic parameters of these BHs in the inner and outer event horizons. We also obtained information about the left and right central charges. We showed that the central charges are not independent of the mass, i.e., they do not correspond to the conformal field theory (CFT). Also, we showed that the two sides of the central charge for the Taub-NUT BH are the same. These results play an important role in improving AdS/CFT and holography and thermodynamic studies. Finally, we compared our results with the other works in the literature. [ABSTRACT FROM AUTHOR]

We explore non-equilibrium processes in two-dimensional conformal field theories (2d CFTs) due to the growth of operators induced by inhomogeneous and homogeneous Hamiltonians by investigating the time dependence of the partition function, energy density, and entanglement entropy. The non-equilibrium processes considered in this paper are constructed out of the Lorentzian and Euclidean time evolution governed by different Hamiltonians. We explore the effect of the time ordering on entanglement dynamics so that we find that in a free boson CFT and RCFTs, this time ordering does not affect the entanglement entropy, while in the holographic CFTs, it does. Our main finding is that in the holographic CFTs, the non-unitary time evolution induced by the inhomogeneous Hamiltonian can retain the initial state information longer than in the unitary time evolution. [ABSTRACT FROM AUTHOR]

Despite the rich and fruitful history of the integrability approach to string theory on the AdS3 × S3 × T4 background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. In other integrable superstring backgrounds there is compelling evidence that this formulation captures all wrapping effects exactly and describes the full planar spectrum. This great success motivates us to study the new proposed QSC and develop methods to extract from it concrete predictions for spectral data. The AdS3 × S3 × T4 case presents a significant novel feature and challenge compared to its higher-dimensional analogues — massless modes. It has been conjectured that these manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N = 4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for unprotected string excitations in the planar limit with finite quantum numbers and RR flux. We explain how to extract a systematic expansion around the analogue of the weak 't Hooft coupling limit in N = 4 SYM and also obtain high-precision numerical results. These concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT. [ABSTRACT FROM AUTHOR]

In two recent papers [1-2] we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised T T ¯ -deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to T T ¯ -perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for T T ¯ -perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of the recent publication [3] where the same problem has been addressed. [ABSTRACT FROM AUTHOR]

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper. [ABSTRACT FROM AUTHOR]

The finite-difference time-domain (FDTD) method is a versatile electromagnetic simulation technique, widely used for solving various broadband problems. However, when dealing with complex structures and large dimensions, especially when applying perfectly matched layer (PML) absorbing boundaries, tremendous computational burdens will occur. To reduce the computational time and memory, this paper presents a Message Passing Interface (MPI) parallel scheme based on non-uniform conformal FDTD, which is suitable for convolutional perfectly matched layer (CPML) absorbing boundaries, and adopts a domain decomposition approach, dividing the entire computational domain into several subdomains. More importantly, only one magnetic field exchange is required during the iterations, and the electric field update is divided into internal and external parts, facilitating the synchronous communication of magnetic fields between adjacent subdomains and internal electric field updates. Finally, unmanned helicopters, helical antennas, 100-period folded waveguides, and 16 × 16 phased array antennas are designed to verify the accuracy and efficiency of the algorithm. Moreover, we conducted parallel tests on a supercomputing platform, showing its satisfactory reduction in computational time and excellent parallel efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we make use of holographic Boundary Conformal Field Theory (BCFT) to simulate the black hole information problem in the semi-classical picture. We investigate the correlation between a portion of Hawking radiation and entanglement islands by the area of an entanglement wedge cross-section. Building on the understanding of the relationship between entanglement wedge cross-sections and perfect tensor entanglement as discussed in reference [18], we make an intriguing observation: in the semi-classical picture, the positioning of an entanglement island automatically yields a pattern of perfect tensor entanglement. Furthermore, the contribution of this perfect tensor entanglement, combined with the bipartite entanglement contribution, precisely determines the area of the entanglement wedge cross-section. [ABSTRACT FROM AUTHOR]

The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, large N factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique. [ABSTRACT FROM AUTHOR]

Recent studies on the holographic descriptions of Kerr black holes indicate that the conformal or the warped conformal symmetries are responsible for the Kerr black hole physics at both background and perturbation levels. In the present paper, we extend the validity of these studies to the case of accelerating Kerr black hole. By invoking a set of non-trivial diffeomorphisms near the horizon bifurcation surface of the accelerating Kerr black hole, the Dirac brackets among charges of the diffeomorphisms form the symmetry algebra of a warped CFT which consists of one Virasoro and one Kac-Moody algebra with central extensions. This provides the evidence for warped CFTs being possible holographic dual to accelerating Kerr black holes. The thermal entropy formula of the warped CFT fixed by modular parameters and vacuum charges reproduces the entropy of the rotating black hole with acceleration. [ABSTRACT FROM AUTHOR]

Our paper presents two main results. First, we study the renormalized free energies of Euclidean Einstein gravity in asymptotically AdS8 and various field theories on a squashed seven sphere. In the gravity theory, we demonstrate the absence of the Hawking-Page transition, while in the field theory, we focus on the O(N) vector model and the massless free fermion model. The conformal symmetry governs the universal behaviors of the free energies for small and large squashings, which we confirm numerically and analytically. Second, we evaluate the second-order derivative of CFT free energy with respect to the squashing parameter, finding universal results that hold for generic conformal field theories. We examine two different squashings, one with an SU(2) bundle, which is the primary focus of our paper, and another with a U(1) bundle, where our results align with the conjectured formula from the gravity side in the literature. [ABSTRACT FROM AUTHOR]

We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as 'arithmetic chaos'. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a 'linear ramp'). We 'bootstrap' the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the dynamics of charge imbalance resolved negativity after a local joining quench in the 1 + 1 dimensional free complex boson CFT. In the first part, we study the local joining quench by applying conformal maps, obtaining analytical universal results. We first calculate the quench dynamics of charged logarithmic negativity. Then using the Fourier transformation, we obtain the charge imbalance resolved negativity. The total negativity can be recovered from the charge-resolved ones. In the second part, we test our CFT predictions against the underlying lattice model numerically. Finally, we explain our results based on the quasi-particle picture. [ABSTRACT FROM AUTHOR]

In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin. [ABSTRACT FROM AUTHOR]

In this paper we study the entanglement entropy in the CFT2, whose gravity dual is AdS3 spacetime with a Chern-Simons term. Using the generalized Rindler method, we obtain the Rindler transformation in the two-dimensional planar CFT and compute the entanglement entropy of the CFT with gravitational anomalies. The conditions under which the entanglement entropy may have anomalous contributions is also discussed. In addition, we present a relatively general form of the Rindler AdS metric and compute its thermal entropy, which agrees with the entanglement entropy in the field theory. Moreover, we utilize the conformal transformation, which maps a cylinder to a plane, to compute the entanglement entropy of the CFT residing on a cylinder, as well as the entanglement entropy of the CFT at finite temperature on a plane. The corresponding contribution of the Chern-Simons term in gravity to the black hole thermal entropy is also obtained from this approach. These results are important for further understandings of the two-dimensional CFT with gravitational anomalies. [ABSTRACT FROM AUTHOR]

In the present paper, we consider quantum theories obtained through the quantization of classical theories with first-class constraints assuming that these constraints form a Lie algebra. We show that in this case, one can construct physical quantities of a new type. We apply this construction to string theory. We find that scattering amplitudes in critical bosonic closed string theory can be expressed in terms of physical quantities of the new type. Our techniques can also be applied to superstrings and heterotic strings. [ABSTRACT FROM AUTHOR]

This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics, quantum field theory, quantum information, and two-dimensional conformal field theory. [ABSTRACT FROM AUTHOR]

In this paper we study the tree-level OPE between two positive helicity outgoing gluons in the celestial CFT for the Yang-Mills theory chirally coupled to a massive scalar background. This theory breaks the translation as well as scale invariance. We compute the subleading terms in the OPE expansion and show that they are same as the subleading terms of the OPE expansions in the MHV sector. As a result the amplitudes of this theory also satisfy the set of differential equations obtained previously for MHV amplitudes in pure YM theory. This is not surprising because the symmetries coming from the leading and subleading soft gluon theorems do not change in the presence of a massive scalar background. [ABSTRACT FROM AUTHOR]

Quantitative theoretical techniques for understanding the substructure of jets at the LHC enable new insights into the dynamics of QCD, and novel approaches to search for new physics. Recently, there has been a program to reformulate jet substructure in terms of correlation functions, E n → 1 E n → 2 ⋯ E n → k , of light-ray operators, E n → , allowing the application of techniques developed in the study of Conformal Field Theories (CFTs). In this paper we further develop these techniques in the particular context of the three-point correlator E n → 1 E n → 2 E n → 3 , using recently computed perturbative data in both QCD and N = 4 sYM. We derive the celestial blocks appearing in the light-ray operator product expansion (OPE) of the three-point correlator, and use the Lorentzian inversion formula to extract the spectrum of light-ray operators appearing in the expansion, showing, in particular, that the OPE data is analytic in transverse spin. Throughout our presentation, we highlight the relation between the OPE approach, and more standard splitting function based approaches of perturbative QCD, emphasizing the utility of the OPE approach for incorporating symmetries in jet substructure calculations. We hope that our presentation introduces a number of new techniques to the jet substructure community, and also illustrates the phenomenological relevance of the study of light-ray operators in the OPE limit to the CFT community. [ABSTRACT FROM AUTHOR]

Conformal theories of the Argyres-Douglas type are notoriously hard to study given that they are isolated and strongly coupled thus lacking a lagrangian description. In flat space, an exact description is provided by the Seiberg-Witten theory. Turning on a Ω-background makes the geometry "quantum" and tractable only in the weak curvature limit. In this paper we use the AGT correspondence to derive Ω-exact formulae for the partition function, in the nearby of monopole points where the dynamics is described by irregular conformal blocks of the CFT. The results are checked against those obtained by the recursion relations coming from a conformal anomaly in the region where the two approaches overlap. The Nekrasov-Shatashvili limit is also discussed. Finally, we comment on the existence of black holes in De Sitter space whose low energy dynamics is described by an Argyres-Douglas theory. [ABSTRACT FROM AUTHOR]

The Charge Convexity Conjecture (CCC) states that in a unitary conformal field theory in d ≥ 3 dimensions with a global symmetry, the minimal dimension of operators in certain representations of the symmetry, as a function of the charge q of the representation (or a generalized notion of it), should be convex. More precisely, this was conjectured to be true when q is restricted to positive integer multiples of some integer q0. The CCC was tested on a number of examples, most of which are in d < 4 dimensions, and its version in which q0 is taken to be the charge of the lowest-dimension positively-charged operator was shown to hold in all of them. In this paper we test the conjecture in a non-trivial example of a d = 4 theory, which is the family of Caswell-Banks-Zaks IR fixed points of SU(Nc) gauge theory coupled to Nf massless fermions and Ns massless scalars. In these theories, the lowest-dimension gauge-invariant operators that transform non-trivially under the global symmetry are mesons. These may consist of two scalars, two fermions or one of each. We find that the CCC holds in all applicable cases, providing significant new evidence for its validity, and suggesting a stronger version for non-simple global symmetry groups. [ABSTRACT FROM AUTHOR]

We study the correlation functions of local operators in unitary T T ¯ -deformed field theories, using their formulation in terms of Jackiw-Teitelboim gravity. The position of the operators is defined using the dynamical coordinates of this formalism. We focus on the two-point correlation function in momentum space, when the undeformed theory is a conformal field theory. In particular, we compute the large momentum behavior of the correlation functions, which manifests the non-locality of the T T ¯ -deformed theory. The correlation function has UV-divergences, which are regulated by a point-splitting regulator. Renormalizing the operators requires multiplicative factors depending on the momentum, unlike the behavior in local QFTs. The large momentum limit of the correlator, which is the main result of this paper, is proportional to q − q 2 π Λ , where q is the momentum and 1/|Λ| is the deformation parameter. Interestingly, the exponent here has a different sign from earlier results obtained by resummation of small q computations. The decay at large momentum implies that the operators behave non-locally at the scale set by the deformation parameter. [ABSTRACT FROM AUTHOR]

In this paper we study uncharged, non-conformal and anisotropic systems with strong interactions using the gauge-gravity duality by considering Einstein-Quadratic-Axion-Dilaton action in five dimension. In fact we would like to gain insight into the influence of higher derivative gravity on the QCD system. At finite temperature, we obtain an anisotropic black brane solution to a 5D Einstein–Gauss–Bonnet-Axion-Dilaton system. The system has been investigated and the effect of the parameter of theory has been considered. The blackening function supports the thermodynamical phase transition between small/large and AdS/large black brane for suitable parameters. We also study transport and diffusion properties, and observe in particular that the butterfly velocity that characterizes both diffusion and growth of chaos transverse to the anisotropic direction saturates a constant value in the IR which can exceed the bound given by the conformal value. We also determine the imaginary part of the heavy quark potential in a strongly coupled plasma dual to Gauss–Bonnet gravity. [ABSTRACT FROM AUTHOR]

We initiate the analytical functional bootstrap study of conformal field theories with large N limits. In this first paper we particularly focus on the 1D O(N) vector bootstrap. We obtain a remarkably simple bootstrap equation from the O(N) vector crossing equations in the large N limit. The numerical conformal bootstrap bound is saturated by the generalized free field theories, while its extremal functional actions do not converge to any non-vanishing limit. We study the analytical extremal functionals of this crossing equation, for which the total positivity of the SL(2, ℝ) conformal block plays a critical role. We prove the SL(2, ℝ) conformal block is totally positive in the limits with large ∆ or small 1 − z and show that the total positivity is violated below a critical value ∆ TP ∗ ≈ 0.32315626. The SL(2, ℝ) conformal block forms a surprisingly sophisticated mathematical structure, which for instance can violate total positivity at the order 10−5654 for a normal value ∆ = 0.1627! We construct a series of analytical functionals {αM} which satisfy the bootstrap positive conditions up to a range ∆ ⩽ ΛM. The functionals {αM} have a trivial large M limit. However, due to total positivity, they can approach the large M limit in a way consistent with the bootstrap positive conditions for arbitrarily high ΛM. Moreover, in the region ∆ ⩽ ΛM, the analytical functional actions are consistent with the numerical bootstrap results, therefore it clarifies the positive structure in the crossing equation analytically. Our result provides a concrete example to illustrate how the analytical properties of the conformal block lead to nontrivial bootstrap bounds. We expect this work paves the way for large N analytical functional bootstrap in higher dimensions. [ABSTRACT FROM AUTHOR]

The symmetric orbifold of 핋4 is the analogue of free SYM in four dimensions, and its dual is described by a tensionless string propagating in AdS3 × S3 × 핋4. In this paper we study the deformation of this exact AdS/CFT duality away from the free point. On the symmetric orbifold side this amounts to perturbing the theory by the exactly marginal operator from the 2-cycle twisted sector. We identify the corresponding perturbation in the dual worldsheet description, and show that the anomalous conformal dimensions of a number of symmetric orbifold currents are correctly reproduced from this worldsheet perspective. [ABSTRACT FROM AUTHOR]

In this paper, we investigate gluing together two Anti-de Sitter (AdS) geometries along a timelike brane, which corresponds to coupling two brane field theories (BFTs) through gravitational interactions in the dual holographic perspective. By exploring the general conditions for this gluing process, we show that the energy stress tensors of the BFTs backreact on the dynamical metric in a manner reminiscent of the TTbar deformation. In particular, we present explicit solutions for the three-dimensional case with chiral excitations and further construct perturbative solutions with non-chiral excitations. [ABSTRACT FROM AUTHOR]

Non-relativistic conformal field theory is significant to understand various aspects of an ultra-cold system. In this paper, we study a non-relativistic system of two-component fermions interacting with a complex boson with Yukawa-like interactions near d = 4-spatial dimensions in the presence of a quenched disorder. The homogeneous theory flows to an interacting fixed point describing a unitary fermion system. In the presence of the disorder, we find that the system has an interesting phase structure in the space of the coupling constants and exhibits an interacting disorder fixed point in ϵ-expansion. The correlation function obeys Lifshitz scaling behaviour at the disorder fixed point with the anisotropic exponent being z = 2 + γE. We also study the disorder system at finite temperature and compute the leading contribution to the 1PI effective action. [ABSTRACT FROM AUTHOR]

We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N = 4 SYM. In this paper, we consider the 1D defect CFT defined on a 1 2 -BPS Wilson line in the theory, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions — known analytically from the QSC. Combining these new constraints and the spectrum of the 10 lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constant of the first non-protected state, giving this observable with seven digits precision for the 't Hooft coupling in the intermediate coupling region λ 4 π ~ 1 , with the error decreasing quickly at large 't Hooft coupling. Furthermore, for the same structure constant we obtain a 4-loop analytic result at weak coupling. We also present results for excited states. [ABSTRACT FROM AUTHOR]

In this paper, we study the fine structure of entanglement in holographic two-dimensional boundary conformal field theories (BCFT) in terms of the spatially resolved quasilocal extension of entanglement entropy — entanglement contour. We find that the boundary induces discontinuities in the contour revealing hidden localization-delocalization patterns of the entanglement degrees of freedom. Moreover, we observe the formation of “islands” where the entanglement contour vanishes identically implying that these regions do not contribute to the entanglement at all. We argue that these phenomena are the manifestation of the entanglement islands recently discussed in the literature. We apply the entanglement contour proposal to the recently discussed BCFT black hole models reproducing the Page curve — moving mirror model and the pair of BCFT in the thermofield double state. From the viewpoint of entanglement contour, the Page curve also carries the imprint of strong delocalization caused by dynamical entanglement islands. [ABSTRACT FROM AUTHOR]

The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci–Yamabe metric and conformal η -Ricci–Yamabe metric. We delineate the conditions for conformal Ricci–Yamabe soliton to be expanding, steady or shrinking. We also discuss conformal Ricci–Yamabe soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid and radiation era. Furthermore, we design conformal η -Ricci–Yamabe soliton to find its characteristics in a perfect fluid spacetime and lastly acquired Laplace equation from conformal η -Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Overall, the main novelty of the paper is to study the geometrical phenomena and characteristics of our newly introduced conformal Ricci–Yamabe and conformal η -Ricci–Yamabe solitons to apply their existence in a perfect fluid spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension D, the four-point function of identical scalar operators ϕ with scaling dimension ∆ϕ such that ∆ϕ/D < 3/4, is necessarily that of the generalized free field theory. This result follows only from crossing symmetry and unitarity. In particular, we do not impose the existence of a conserved spin two operator (stress tensor). We also present an argument to extend the applicability of this result to a larger range of conformal dimensions, namely to ∆ϕ/D < 1. This extension requires some reasonable assumptions about the spectrum of light operators. Together, these results suggest that if there is a non-trivial conformal theory in large dimensions, not necessarily having a stress tensor, then its relevant operators must be exponentially weakly coupled with the rest. [ABSTRACT FROM AUTHOR]

In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the SD−1 spatial slice in radial quantization in D = 2, 3 dimensions. In each case, we use the conformal Ward Identities to solve systematically for the Fourier components. We then use these Fourier components to build conformal blocks for the four-point function in momentum space, giving a finite-volume version of the momentum-space conformal blocks. We check that this construction is consistent with the known result in infinite volume. Our construction may help to find bootstrap equations that can give nontrivial constraints that do not appear in analysis in infinite volume. We show some examples of bootstrap equations and their nontriviality. [ABSTRACT FROM AUTHOR]

Recently introduced connections between quantum codes and Narain CFTs provide a simple ansatz to express a modular-invariant function Z τ τ ¯ in terms of a multivariate polynomial satisfying certain additional properties. These properties include algebraic identities, which ensure modular invariance of Z τ τ ¯ , and positivity and integrality of coefficients, which imply positivity and integrality of the 픲(1)n × 픲(1)n character expansion of Z τ τ ¯ . Such polynomials come naturally from codes, in the sense that each code of a certain type gives rise to the so-called enumerator polynomial, which automatically satisfies all necessary properties, while the resulting Z τ τ ¯ is the partition function of the code CFT — the Narain theory unambiguously constructed from the code. Yet there are also "fake" polynomials satisfying all necessary properties, that are not associated with any code. They lead to Z τ τ ¯ satisfying all modular bootstrap constraints (modular invariance and positivity and integrality of character expansion), but whether they are partition functions of any actual CFT is unclear. We consider the group of the six simplest fake polynomials and denounce the corresponding Z's as fake: we show that none of them is the torus partition function of any Narain theory. Moreover, four of them are not partition functions of any unitary 2d CFT; our analysis for other two is inconclusive. Our findings point to an obvious limitation of the modular bootstrap approach: not every solution of the full set of torus modular bootstrap constraints is due to an actual CFT. In the paper we consider six simple examples, keeping in mind that thousands more can be constructed. [ABSTRACT FROM AUTHOR]

In this paper, we show that bulk reconstruction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is rather simple and has an intuitive picture, by showing that the HKLL (Hamilton-Kabat-Lifschytz-Lowe) bulk reconstruction formula can be simplified. We also reconstruct the wave packets in the bulk theory from the CFT primary operators. With these wave packets, we discuss the causality and duality constraints and find our picture is the only consistent one. Our picture of the bulk reconstruction can be applied to the asymptotic AdS spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we consider how to formulate semiclassical problems in the context of the AdS/CFT correspondence, based on the proposal of Compere and Marolf. Our prescription involves the effective action with self-action term for boundary dynamical fields, which can be viewed as imposing mixed boundary conditions for the gravity dual. We derive the semiclassical Einstein equations sourced by boundary CFT stress-energy tensor. Analyzing perturbations of the holographic semiclassical Einstein equations, we find a universal parameter γd which controls the contribution from boundary CFTs and specifies dynamics on the AdS boundary. As a simple example, we examine the semiclassical Einstein equations in 3-dimensions with 4-dimensional AdS gravity dual, and show that the boundary BTZ black hole with vanishing expectation value of the stress-energy tensor becomes unstable due to the backreaction from quantum stress-energy tensor when the parameter γd exceeds a certain critical value. [ABSTRACT FROM AUTHOR]

De-Sitter(dS) space allows for a generalized class of vacua, known as α–vacua, described by some parameters. The Bunch-Davies (BD) vacuum is a point in this parameter space. The cosmological correlation function in BD vacuum in four dimensions and can be interpreted as CFT3 correlation function of certain operators. However, the correlation function in α–vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in α–vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the α–vacua can be related to three-dimensional CFT correlation functions if we relax the requirement of consistency with OPE limit. Relaxation of consistency with OPE limit can be naturally achieved in momentum space. [ABSTRACT FROM AUTHOR]

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector. [ABSTRACT FROM AUTHOR]

We compute a large collection of string worldsheet correlators describing light probes interacting with heavy black hole microstates. The heavy states consist of NS5 branes carrying momentum and/or fundamental string charge. In the fivebrane decoupling limit, worldsheet string theory on a family of such backgrounds is given by exactly solvable null-gauged WZW models. We construct physical vertex operators in these cosets, including all massless fluctuations. We compute a large class of novel heavy-light-light-heavy correlators in the AdS3 limit, where the light operators include those dual to chiral primaries of the holographically dual CFT. We compare a subset of these correlators to the holographic CFT at the symmetric product orbifold point, and find precise agreement in all cases, including for light operators in twisted sectors of the orbifold CFT. The agreement is highly non-trivial, and includes amplitudes that describe the analogue of Hawking radiation for these microstates. We further derive a formula for worldsheet correlators consisting of n light insertions on these backgrounds, and discuss which subset of these correlators are likely to be protected. As a test, we compute a heavy-light five-point function, obtaining precisely the same result both from the worldsheet and the symmetric orbifold CFT. This paper is a companion to and extension of [1]. [ABSTRACT FROM AUTHOR]

In previous work we constructed an explicit mapping between large N vector models (free or critical) in d dimensions and a non-local high-spin gravity theory on AdSd+1, such that the gravitational theory reproduces the field theory correlation functions order by order in 1/N. In this paper we discuss three aspects of this mapping. First, our original mapping was not valid non-perturbatively in 1/N, since it did not include non- local correlations between the gravity fields which appear at finite N. We show that by using a bi-local G − Σ type formalism similar to the one used in the SYK model, we can construct an exact mapping to the bulk that is valid also at finite N. The theory in the bulk contains additional auxiliary fields which implement the finite N constraints. Second, we discuss the generalization of our mapping to the field theory on Sd, and in particular how the sphere free energy matches exactly between the two sides, and how the mapping can be consistently regularized. Finally, we discuss the field theory at finite temperature, and show that the low-temperature phase of the vector models can be mapped to a high-spin gravity theory on thermal AdS space. [ABSTRACT FROM AUTHOR]

We derive correspondences of correlation functions among dual conformal field theories in two dimensions by developing a “first order formulation” of coset models. We examine several examples, and the most fundamental one may be a conjectural equivalence between a coset (SL(n)k ⊗SL(n)−1)/SL(n)k−1 and sl n Toda field theory with generic level k. Among others, we also complete the derivation of higher rank FZZ-duality involving a coset SL(n + 1)k /(SL(n)k ⊗ U(1)), which could be done only for n = 2, 3 in our previous paper. One obstacle in the previous work was our poor understanding of a first order formulation of coset models. In this paper, we establish such a formulation using the BRST formalism. With our better understanding, we successfully derive correlator correspondences of dual models including the examples mentioned above. The dualities may be regarded as conformal field theory realizations of some of the Gaiotto-Rapčák dualities of corner vertex operator algebras. [ABSTRACT FROM AUTHOR]

In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers [n,l]. n is the number of characters of the RCFT as well as the order of the MLDE that the characters solve and l, the Wronskian index, is associated to the structure of the zeroes of the Wronskian of the characters. In this paper, we study [3,0] and [3,2] MLDEs in order to classify the corresponding CFTs. We reduce the problem to a “finite” problem: to classify CFTs with central charge 0 < c ≤ 96, we need to perform 6, 720 computations for the former and 20, 160 for the latter. Each computation involves (i) first finding a simultaneous solution to a pair of Diophantine equations and (ii) computing Fourier coefficients to a high order and checking for positivity. In the [3,0] case, for 0 < c ≤ 96, we obtain many character-like solutions: two infinite classes and a discrete set of 303. After accounting for various categories of known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras and Gaberdiel-Hampapura-Mukhi novel coset CFTs, we seem to have seven hitherto unknown character-like solutions which could potentially give new CFTs. We also classify [3,2] CFTs for 0 < c ≤ 96: each CFT in this case is obtained by adjoining a constant character to a [2,0] CFT, whose classification was achieved by Mathur-Mukhi-Sen three decades ago. [ABSTRACT FROM AUTHOR]

We study SU(2) Chern-Simons theories at level k coupled to a scalar on T2 × ℝ at large baryon number. We find a homogeneous but anisotropic ground state configuration for any values of k on the IR fixed-point of those models. This classical analysis is valid as long as we take the baryon number large. As a corollary, by comparing the symmetry breaking pattern at large chemical potential, we find that the theory does not reduce to the singlet sector of the O(4) Wilson-Fisher fixed-point at large-k, as expected from general grounds. This paper will be one primitive step towards quantitative analysis of Chern-Simons-matter dualities using the large charge expansion. [ABSTRACT FROM AUTHOR]

We study how coarse-graining procedure of an underlying UV-complete quantum gravity gives rise to a connected geometry. It has been shown, quantum entanglement plays a key role in the emergence of such a geometric structure, namely a smooth Einstein-Rosen bridge. In this paper, we explore the possibility of the emergence of similar geometric structure from classical correlation, in the AdS/CFT setup. To this end, we consider a setup where we have two decoupled CFT Hilbert spaces, then choose a random typical state in one of the Hilbert spaces and the same state in the other. The total state in the fine-grained picture is of course a tensor product state, but averaging over the states sharing the same random coefficients creates a geometric connection for simple probes. Then, the apparent spatial wormhole causes a factorization puzzle. We argue that there is a spatial analog of half-wormholes, which resolves the puzzle in the similar way as the spacetime half-wormholes. [ABSTRACT FROM AUTHOR]

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds. [ABSTRACT FROM AUTHOR]

Recently, a method was described for deriving Holographic RG equation in AdSD+1 space starting from an Exact RG equation of a D-dimensional boundary CFT [22]. The evolution operator corresponding to the Exact RG equation was rewritten as a functional integral of a D + 1 dimensional field theory in AdSD+1 space. This method has since been applied to elementary scalars and composite scalars in the O(N) model [34]. In this paper, we apply this technique to the conserved vector current and the energy momentum tensor of a boundary CFT, the O(N) model at a fixed point. These composite spin one and spin two operators are represented by auxiliary fields and extend into the bulk as gauge fields and metric perturbations. We obtain, at the free level, the (gauge fixed) Maxwell and Einstein actions. While the steps involved are motivated by the AdS/CFT correspondence, none of the steps logically require the AdS/CFT conjecture for their justification. [ABSTRACT FROM AUTHOR]

Conformal Quantum Field Theories (CFT) in 1 or 1+1 spacetime dimensions (respectively called chiral and full CFTs) admit several "axiomatic" (mathematically rigorous and model-independent) formulations. In this note, we deal with the von Neumann algebraic formulation due to Haag and Kastler [43], mainly restricted to the chiral CFT setting [18]. Irrespectively of the chosen formulation, one can ask the question s: given a theory A, how many and which are the possible extensions B ⊃ A or subtheories B ⊂ A? How to construct and classify them, and study their properties? Extensions are typically described in the language of algebra objects in the braided tensor category of representations of A, while subtheories require different ideas. In this paper, we review recent structural results on the study of subtheories in the von Neumann algebraic formulation (conformal subnets) of a given chiral CFT (conformal net), [4], [5], [6], [7]. Furthermore, building on [7], we provide a "quantum Galois theory" for conformal nets analogous to the one for Vertex Operator Algebras (VOA) [28], [29]. We also outline the case of 3+1 dimensional Algebraic Quantum Field Theories (AQFT). The aforementioned results make use of families of (extreme) vacuum state preserving unital completely positive maps acting on the net of von Neumann algebras, hereafter called quantum operations. These are natural generalizations of the ordinary vacuum preserving gauge automorphisms, hence they play the role of "generalized global gauge symmetries". Quantum operations suffice to describe all possible conformal subnets of a given conformal net with the same central charge. [ABSTRACT FROM AUTHOR]

The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the N = 4 SYM case, as we speculate in the last part of the article. [ABSTRACT FROM AUTHOR]

This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge. [ABSTRACT FROM AUTHOR]

The recent paper [1] described how states of a holographic CFT can be approximated by states of a large collection of non-interacting BCFTs, such that the dual of the new system accurately approximates an arbitrarily large causal patch of the original geometry. In this paper, we first describe in more detail the geometries dual to such discrete BCFT systems, emphasizing that they are multi-boundary wormholes in which it is not possible to move causally between different asymptotic regions. By reintroducing couplings between the BCFTs in various ways, we show that the wormholes can be made traversable, giving an intermediate class of geometries that interpolate between the multi-boundary wormhole and the original geometry that it approximates. [ABSTRACT FROM AUTHOR]