The thermodynamic stability of large AdS$_3$ black holes implies that Cardy's $Δ\rightarrow\infty$ formula for the density of states remains approximately valid when $Δ\sim c$ in holographic 2d CFTs, constraining their light spectra. Averaged OPE coefficients take a similarly universal asymptotic form, and black hole arguments again imply an extended regime of validity. In this note we study conditions under which the OPE asymptotics extend to $Δ\sim c$ at large central charge. Some of the conditions found are stronger than required by an extended Cardy regime and are violated by permutation orbifolds, such as the D1-D5 system at zero coupling. Our results suggest new bounds on non-vacuum block contributions to correlation functions in holographic CFTs.
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to renormalized position space correlators. Several applications are presented, including the holographic boundary CFTs as well as spacelike boundary CFTs, which provide realizations of the pseudo-conformal universe.
We present a large class of holographic models where the boundary ${\mathbb R}^{2,1}$ dimensional conformal field theory has a thermal phase with a spontaneously broken global symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ violate the no-hair theorem.
In this work, we study the holographic entanglement entropy of two dimensional $T\bar{T}$-deformed conformal field theory. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of New massive gravity, General minimal massive gravity, and Exotic general massive gravity. We also apply Song's prescription to obtain the entanglement entropy for deformed theories. In each cases, we find agreement between the results.
The behavior of holographic CFTs is constrained by the existence of a bulk dual geometry. For example, in (2+1)-dimensional holographic CFTs living on a static spacetime with compact spatial slices, the vacuum energy must be nonpositive, certain averaged energy densities must be nonpositive, and the spectrum of scalar operators is bounded from below by the Ricci scalar of the CFT geometry. Are these results special to holographic CFTs? Here we show that for perturbations about appropriate backgrounds, they are in fact universal to all CFTs, as they follow from the universal behavior of two- an…
We develop a first order formalism for constructing gravitational duals of conformal defects in a bottom up approach. Similarly as for the flat domain walls a single function specifies the solution completely. Using this formalism we construct several novel families of analytic solutions dual to conformal interfaces and boundaries. As a sample application we study the boundary OPE and entanglement entropy for one of the found defects.
By relaxing the regularity conditions imposed in arXiv:1107.1722 on half-BPS solutions to six-dimensional Type~4b supergravity, we enlarge the space of solutions to include two new half-BPS configurations, which we refer to as the \kap\ and the \funnel. We give evidence that the \kap\ and \funnel\ can be interpreted as fully back-reacted brane solutions with respectively $AdS_2$ and $AdS_2\times S^2$ world volumes. \kap\ and \funnel\ solutions with a single asymptotic $AdS_3 \times S^3$ region are constructed analytically. We argue that \kap\ solutions provide simple examples of holographic du…
We investigate some aspects of a recent proposal for a holographic description of the multiverse. Specifically, we focus on the implications on the suggested duality of the fluctuations of a bubble separating two universes with different cosmological constants. We do so by considering a similar problem in a 2+1 CFT with a codimension one defect, obtained by an M5-brane probe embedding in AdS_4x S^7, and studying its spectrum of fluctuations. Our results suggest that the kind of behavior required by the spectrum of bubble fluctuations is not likely to take place in defect CFTs with an AdS dual,…
There appears a universal logarithmic term of entanglement entropy, i.e., $-a(Ω) \log(H/δ)$, for 3d CFTs when the entangling surface has a sharp corner. $a(Ω)$ is a function of the corner opening angle and behaves as $a(Ω\to π)\simeq σ(π-Ω)^2$ and $a(Ω\to 0)\simeq κ/Ω$, respectively. Recently, it is conjectured that $σ/C_T=π^2/24 $, where $C_T$ is central charge in the stress tensor correlator, is universal for general CFTs in three dimensions. In this paper, by applying the general higher curvature gravity, we give a holographic proof of this conjecture. We also clarify some interesting probl…
We discuss the concepts of mutual and tripartite information by referring to simple intuitive examples, and describe their use as probes of thermalization in holographic models. We then review our computation of these quantities in a simple time dependent model, in which energy injection in a strongly coupled field theory is modeled by a shell of null dust falling into 3d anti-de Sitter space. We complete those results with a discussion of the possible equilibrium phases of the tripartite information.
We use modular invariance to derive constraints on the spectrum of warped conformal field theories (WCFTs) --- nonrelativistic quantum field theories described by a chiral Virasoro and $U(1)$ Kac-Moody algebra. We focus on holographic WCFTs and interpret our results in the simplest holographic set up: three dimensional gravity with Compere-Song-Strominger boundary conditions. Holographic WCFTs feature a negative $U(1)$ level that is responsible for negative norm descendant states. Despite the violation of unitarity we show that the modular bootstrap is still viable provided the (Virasoro-Kac-M…
Thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, $λ_L\leq 2π/β$. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how $λ_L=2π/β$ in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge and a set of high…
Solutions of $(d+1)$-dimensional gravity coupled to a scalar field are obtained, which holographically realize interface and boundary CFTs. The solution utilizes a Janus-like $\mathrm{AdS}_d$ slicing ansatz and corresponds to a deformation of the CFT by a spatially-dependent coupling of a relevant operator. The BCFT solutions are singular in the bulk, but physical quantities such as the holographic entanglement entropy can be calculated.
New families of regular half-BPS solutions to 6-dimensional Type 4b supergravity with $m$ tensor multiplets are constructed exactly. Their space-time consists of $AdS_2 \times S^2$ warped over a Riemann surface with an arbitrary number of boundary components, and arbitrary genus. The solutions have an arbitrary number of asymptotic $AdS_3 \times S^3$ regions. In addition to strictly single-valued solutions to the supergravity equations whose scalars live in the coset $SO(5,m)/SO(5)\times SO(m)$, we also construct stringy solutions whose scalar fields are single-valued up to transformations und…
The study of Rényi mutual information (RMI) sheds light on the AdS/CFT correspondence beyond classical order. In this article, we study the Rényi mutual information between two intervals at large distance in two-dimensional holographic warped conformal field theory, which is conjectured to be dual to the gravity on AdS3 or warped AdS3 spacetime under the Dirichlet-Newman boundary conditions. By using the operator product expansion of twist operators up to level 3, we read the leading oder and the next-toleading order RMI in the large central charge and small cross-ratio limits. The leading ord…
We calculate the Rényi entropy $S_q(μ,λ)$, for a spherical entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings $λ$, larger than a specific value, but still allowed by causality, we observe a violation of the inequality $\frac{\partial}{\partial q}\left({\frac{q - 1}{q}S_q(μ,λ)} \right) \ge 0$, which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction o…
We discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators factorize. We demonstrate that factorization can only hold in the large central charge limit. Using conformal invariance and factorization we argue that these operators are naturally represented as fields in AdS as this makes the underlying linearity of the system manifest. In this class of CFTs the solution of the conformal bootstrap conditions can be naturally organized in structures which coincide with W…
Entanglement entropy obeys a 'first law', an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entangleme…
Since many thermodynamic properties of black holes are universal, the thermodynamics of their holographic duals should be universal too. We show how this universality is exhibited in the example of symmetric orbifolds of general two dimensional CFTs. We discuss the free energies and phase diagrams of such theories and show that they are indeed universal in the large N limit. We also comment on the implications of our results for the classification of CFTs that can have an interpretation as holographic duals to gravity theories on AdS(3).
We consider general planar deformations of a circular distribution of NS5-branes. The near-horizon region of the latter admits, after a T-duality transformation, an exact conformal-field-theory description in terms of the coset model SU(2)/U(1) X SL(2,R)/U(1). We derive the exactly marginal operators corresponding to an infinitesimal planar deformation using the conjectured holography between the coset model and the little string theory that resides on the worldvolume of the NS5-branes. Subsequently, we perform a complementary analysis of the same deformations using the associated N=1 supersym…
We present a constructive derivation of holographic four-point correlators of arbitrary half-BPS operators for all maximally supersymmetric conformal field theories in $d>2$. This includes holographic correlators in 3d ${\cal N}=8$ ABJM theories, 4d ${\cal N}=4$ SYM theory and the 6d ${\cal N}=(2,0)$ theory, dual to tree-level amplitudes in 11D supergravity on $AdS_4 \times S^7$, 10D supergravity on $AdS_5 \times S^5$ and 11D supergravity on $AdS_7 \times S^4$, respectively. We introduce the concept of Maximally R-symmetry Violating (MRV) amplitude, which corresponds to a special configuration…
We construct the non-relativistic counterparts of some well-known supergravity solutions dual to relevant and marginal deformations of N=4 super Yang-Mills. The main tool we use is the null Melvin twist and we apply it to the N=1 and N=2* Pilch-Warner RG flow solutions as well as the Lunin-Maldacena solution dual to beta-deformations of N=4 super Yang-Mills. We also obtain a family of supergravity solutions with Schrodinger symmetry interpolating between the non-relativistic version of the N=1 Pilch-Warner and Klebanov-Witten fixed points. A generic feature of these non-relativistic background…
Dynamics in AdS spacetimes is characterized by various time-periodicities. The most obvious of these is the time-periodic evolution of linearized fields, whose normal frequencies form integer-spaced ladders as a direct consequence of the structure of representations of the conformal group. There are also explicitly known time-periodic phenomena on much longer time scales inversely proportional to the coupling in the weakly nonlinear regime. We ask what would correspond to these long time periodicities in a holographic CFT, provided that such a CFT reproducing the AdS bulk dynamics in the large…
We construct non-geometric AdS$_4$ solutions of IIB string theory where the fields in overlapping patches are glued by elements of the S-duality group. We obtain them by suitable quotients of compact and non-compact geometric solutions. The quotient procedure suggests CFT duals as quiver theories with links involving the so-called $T[U(N)]$ theory. We test the validity of the non-geometric solutions (and of our proposed holographic duality) by computing the three-sphere partition function $Z$ of the CFTs. A first class of solutions is obtained by an S-duality quotient of Janus-type non-compact…
The Ryu-Takayanagi (RT) formula has been a key ingredient in our understanding of holography. Recent work on TT deformations has also boosted our understanding of holography away from the conformal boundary of AdS. In this short note, we aim to refine some recent work demonstrating the success of the RT formula in TT deformed theories. We emphasize general arguments that justify the use of the RT formula in general holographic theories that obey a GKPW-like dictionary. In doing so, we clarify subtleties related to holographic counterterms and discuss the implications for holography in general …
Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator $J \bar T$, where $J$ is a chiral $U(1)$ current and $\bar T$ is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its $J \bar T$ deformation. We find that the dual spacetime is still AdS$_3$, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the $U(1)$ current. We show that when the coefficient of the chiral anomaly for $J$ vanis…
We develop a general approach to simplify the derivation of the holographic Weyl anomaly. As an application, we derive the holographic Weyl anomaly from general higher derivative gravity in asymptotically $AdS_{5}$ and $AdS_{7}$. Interestingly, to derive all the central charges of 4d and 6d CFTs, we make no use of equations of motion. Following Myers' idea, we propose a formula of holographic entanglement entropy for higher derivative gravity in asymptotically $AdS_5$. Applying this formula, we obtain the correct universal term of entanglement entropy for 4d CFTs. It turns out that our formula…
In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting $\mathcal{N}=4$ super Yang-Mills theories by introducing a minimal surface in the S$^5$ direction, instead of the AdS$_5$ direction. This offers a possible general…
We compare the behavior of the vacuum free energy (i.e. the Casimir energy) of various $(2+1)$-dimensional CFTs on an ultrastatic spacetime as a function of the spatial geometry. The CFTs we consider are a free Dirac fermion, the conformally-coupled scalar, and a holographic CFT, and we take the spatial geometry to be an axisymmetric deformation of the round sphere. The free energies of the fermion and of the scalar are computed numerically using heat kernel methods; the free energy of the holographic CFT is computed numerically from a static, asymptotically AdS dual geometry using a novel app…
We study the thermodynamic relations of conformal field theories (CFTs), which are holographically dual to anti-de Sitter-Schwarzschild bulk space-times. A Cardy-Verlinde formula is derived thermodynamically for CFTs living on S^n x R with S^n having an arbitrary radius. The Hawking-Page phase transition of the CFT is described using Landau's theory of phase transitions, and an alternative derivation of the Cardy-Verlinde formula is presented. The condensate in the high temperature phase is identified as being composed of radiational matter.
Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge $C_T$, we clarify the properties of stress tensor composite primary operators of minimal twist, $[T^m]$, using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $\langle \mathcal{O}_L\mathcal{O}_L [T^m]\rangle$, where $\mathcal{O}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory …
In this paper we study generic features of nonlocal charges obtained from marginal deformations of WZNW models. Using free-fields representations of CFTs based on simply laced Lie algebras, one can use simple arguments to build the nonlocal charges; but for more general Lie algebras these methods are not strong enough to be generally used. We propose a brute force calculation where the nonlocality is associated to a new Lie algebra valued field, and from this prescription we impose several constraints on the algebra of nonlocal charges. Possible applications for Yang-Baxter and holographic \(T…
Bulk localized excited states in an AdS spacetime can be constructed from Ishibashi states with respect to the global conformal symmetry in the dual CFT. We study boundary two point functions of primary operators in the presence of bulk localized excitations in two dimensional CFTs. From two point functions in holographic CFTs, we observe causal propagations of radiations when the mass of dual bulk scalar field is close to the BF bound. This behavior for holographic CFTs is consistent with the locality and causality in classical gravity duals. We also show that this cannot be seen in free ferm…
We extend our topological renormalization scheme for Entanglement Entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS/CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized Entanglement Entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the Replica Trick to express the renormalized Entanglement Entropy in terms of the renormalized gravitational ac…
Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Gwangju Institute of Science and Technology（光州科学技术院）；National Institute of Technology, Yuge College（国立丰桥技术大学宇部学院）
We derive a general formula for renormalized entanglement entropy in even dimensional CFTs holographically dual to Einstein gravity in one dimension higher. In order to renormalize, we adapt the Kounterterm method to asymptotically locally AdS manifolds with conical singularities. On the gravity side, the computation considers extrinsic counterterms and the use of the replica trick a la Lewkowycz-Maldacena. The boundary counterterm B_d is shown to satisfy a key property, in direct analogy to the Euler density: when evaluated on a conically singular manifold, it decomposes into a regular part p…
Holographic reconstruction for defect CFTs from $\mathrm{AdS}_p \times S^q$ spacetimes
International Centre for Theoretical Physics Asia–Pacific, University of Chinese Academy of Sciences（中国科学院大学亚太理论物理中心）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）
Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
We present a consistent Kaluza-Klein truncation of D=11 supergravity on an arbitrary seven-dimensional Sasaki-Einstein space (SE_7) to a D=4 theory containing a metric, a gauge-field, a complex scalar field and a real scalar field. We use this D=4 theory to construct various black hole solutions that describe the thermodynamics of the d=3 CFTs dual to skew-whiffed AdS_4 X SE_7 solutions. We show that these CFTs have a rich phase diagram, including holographic superconductivity with, generically, broken parity and time reversal invariance. At zero temperature the superconducting solutions are c…
We use the holographic methods to calculate the entanglement entropy for field theories modified by $T\bar{T}$ insertion. Based on the available holographic proposals, this calculation reduces to the holographic computations in AdS with finite cut-off. We perform a direct holographic calculation of the entanglement entropy for two dimensional deformed theory. By direct we mean the evaluation of the gravitational action in the bulk spacetime which has been reconstructed from a dual CFT$_2$ on $n$-sheeted Riemann surface as a finite cut-off boundary. We also apply Ryu-Takayanagi's prescription t…
We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor update…
We study the dynamical evolution of strongly coupled field theories, initially in thermal equilibrium, under the influence of an external driving force. We model the field theory holographically using classical gravitational dynamics in an asymptotically AdS spacetime. The system is driven by a source for a (composite) scalar operator. We focus on a scenario where the external source is periodic in time and chart out the response of several observables. We find an interesting phase structure in the response as a function of the amplitude of the source and driving frequency. Specifically the sy…
We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with $U(1)^c \times U(1)^c$ symmetry and a composite boundary graviton. Additionally, for small central charge $c$, we obtain general constraints on the spectral gap of f…
The holographic duals of higher spin theories on AdS_3 are described by the large N limit of a family of minimal model CFTs, whose symmetry algebra is equivalent to W(infinity)[lambda]. We study perturbations of these limit theories, and show that they possess a marginal symmetry-preserving perturbation that describes switching on the 1/N corrections. We also test our general results for the specific cases of lambda=0,1, where free field realisations are available.
