Showing papers on "AdS/CFT correspondence published in 2018"

How to Succeed at Holographic Correlators Without Really Trying

Abstract: We give a detailed account of the methods introduced in [1] to calculate holographic four-point correlators in IIB supergravity on AdS5 × S5. Our approach relies entirely on general consistency conditions and maximal supersymmetry. We discuss two related methods, one in position space and the other in Mellin space. The position space method is based on the observation that the holographic four-point correlators of one-half BPS single-trace operators can be written as finite sums of contact Witten diagrams. We demonstrate in several examples that imposing the superconformal Ward identity is sufficient to fix the parameters of this ansatz uniquely, avoiding the need for a detailed knowledge of the supergravity effective action. The Mellin space approach is an “on-shell method” inspired by the close analogy between holographic correlators and flat space scattering amplitudes. We conjecture a compact formula for the four-point correlators of one-half BPS single-trace operators of arbitrary weights. Our general formula has the expected analytic structure, obeys the superconformal Ward identity, satisfies the appropriate asymptotic conditions and reproduces all the previously calculated cases. We believe that these conditions determine it uniquely.

Entanglement of purification: from spin chains to holography

Abstract: Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

Quantum gravity from conformal field theory

Abstract: We bootstrap loop corrections to AdS5 supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of $$ \mathcal{N} $$ = 4 super Yang-Mills theory. In particular this yields much new information on the spectrum of double-trace operators which can then be used, in combination with superconformal symmetry and crossing symmetry, to obtain a prediction for the one-loop amplitude for four graviton multiplets in AdS. This in turn yields further new results on subleading O(1/N 4) corrections to certain double-trace anomalous dimensions.

Quantum Transfiguration of Kruskal Black Holes

Abstract: We present a new effective description of macroscopic Kruskal black holes that incorporates corrections due to quantum geometry effects of loop quantum gravity. It encompasses both the "interior" region that contains classical singularities and the "exterior" asymptotic region. Singularities are naturally resolved by the quantum geometry effects of loop quantum gravity, and the resulting quantum extension of the full Kruskal space-time is free of all the known limitations of previous investigations of the Schwarzschild interior. We compare and contrast our results with these investigations and also with the expectations based on the AdS/CFT duality.

Gravitational S-matrix from CFT dispersion relations

Abstract: We analyse the double-discontinuities of the four-point correlator of the stress-tensor multiplet in N=4 SYM at large t’ Hooft coupling and at order 1/N4, as a way to access one-loop effects in the dual supergravity theory. From these singularities we extract CFT-data by using two inversion procedures: one based on a recently proposed Froissart-Gribov inversion integral, and the other based on large spin perturbation theory. Both procedures lead to the same results and are shown to be equivalent more generally. Our computation parallels the standard S-matrix reconstruction via dispersion relations. In a suitable limit, the result of the conformal field theory calculation is compared with the one-loop graviton scattering amplitude in ten-dimensional IIB supergravity in flat space, finding perfect agreement.

Entropy, Extremality, Euclidean Variations, and the Equations of Motion

Abstract: We study the Euclidean gravitational path integral computing the Renyi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton’s constant G N , providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.

Quantum extension of the Kruskal spacetime

Abstract: Loop quantum gravity---a theory that extends general relativity by quantizing spacetime---predicts that black holes evolve into white holes.

The Schwarzian Theory - Origins

Abstract: In this paper we further study the 1d Schwarzian theory, the universal low-energy limit of Sachdev-Ye-Kitaev models, using the link with 2d Liouville theory. We provide a path-integral derivation of the structural link between both theories, and study the relation between 3d gravity, 2d Jackiw-Teitelboim gravity, 2d Liouville and the 1d Schwarzian. We then generalize the Schwarzian double-scaling limit to rational models, relevant for SYK-type models with internal symmetries. We identify the holographic gauge theory as a 2d BF theory and compute correlators of the holographically dual 1d particle-on-a-group action, decomposing these into diagrammatic building blocks, in a manner very similar to the Schwarzian theory.

On the Dynamics of Near-Extremal Black Holes

Abstract: We analyse the dynamics of near-extremal Reissner-Nordstrom black holes in asymptotically four-dimensional Anti de Sitter space (AdS4). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

Cutoff AdS$_{3}$ versus the $ T\overline{T} $ deformation

Abstract: A recent proposal relates two dimensional holographic conformal field theories deformed by the integrable $$ T\overline{T} $$ T T ¯ flow to AdS3 with a finite radial cutoff. We investigate this proposal by studying perturbative correlation functions on the two sides. For low point correlators of the stress tensor, we successfully match the deformed CFT results at large central charge to bulk results obtained in classical pure gravity. The deformed CFT also provides definite predictions for loop corrections in the bulk. We then include matter fields in the bulk. To reproduce the classical bulk two-point function of a scalar operator we show that the deformed CFT needs to be augmented with double trace scalar operators, with the $$ T\overline{T} $$ T T ¯ operator yielding corrections corresponding to loops in the bulk.

A universal counting of black hole microstates in AdS4

Abstract: Many three-dimensional $$ \mathcal{N}=2 $$ SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS4 magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS2 solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.

Holographic complexity in Vaidya spacetimes. Part II

Abstract: We examine holographic complexity in time-dependent Vaidya spacetimes with both the complexity=volume (CV) and complexity=action (CA) proposals. We focus on the evolution of the holographic complexity for a thin shell of null fluid, which collapses into empty AdS space and forms a (one-sided) black hole. In order to apply the CA approach, we introduce an action principle for the null fluid which sources the Vaidya geometries, and we carefully examine the contribution of the null shell to the action. Further, we find that adding a particular counterterm on the null boundaries of the Wheeler-DeWitt patch is essential if the gravitational action is to properly describe the complexity of the boundary state. For both the CV proposal and the CA proposal (with the extra boundary counterterm), the late time limit of the growth rate of the holographic complexity for the one-sided black hole is precisely the same as that found for an eternal black hole.

TASI Lectures on the Emergence of Bulk Physics in AdS/CFT

Abstract: These lectures review recent developments in our understanding of the emergence of local bulk physics in AdS/CFT. The primary topics are sufficient conditions for a conformal field theory to have a semiclassical dual, bulk reconstruction, the quantum error correction interpretation of the correspondence, tensor network models of holography, and the quantum Ryu-Takayanagi formula.

Many-body chaos and energy dynamics in holography

Abstract: Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point ω = iλ, k = iλ/vB in the complex frequency and momentum plane. Here λ and vB are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.

Shockwave S-matrix from Schwarzian Quantum Mechanics

Abstract: Schwarzian quantum mechanics describes the collective IR mode of the SYK model and captures key features of 2D black hole dynamics. Exact results for its correlation functions were obtained in [1]. We compare these results with bulk gravity expectations. We find that the semi-classical limit of the OTO four-point function exactly matches with the scattering amplitude obtained from the Dray-’t Hooft shockwave $$ \mathcal{S} $$ -matrix. We show that the two point function of heavy operators reduces to the semi-classical saddle-point of the Schwarzian action. We also explain a previously noted match between the OTO four point functions and 2D conformal blocks. Generalizations to higher-point functions are discussed.

Effective Field Theory for Chaotic CFTs

Abstract: We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss the gauge symmetries of the model and how they relate to the Lyapunov behaviour of certain correlators. We calculate the out-of-time-ordered correlators diagnosing quantum chaos, as well as certain more fine-grained higher-point generalizations, using our Lorentzian effective field theory. We comment on potential future applications of the effective theory to real-time thermal physics and conformal field theory.

Path Integral Complexity for Perturbed CFTs

Abstract: In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories. Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings. Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence. Last but not the least, we estimate contributions to complexity from relevant perturbations.

Circuit complexity in interacting QFTs and RG flows

Abstract: We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the ϕ4 theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen’s geometric method, which translates into working out the geodesic equation arising from a certain cost functional. We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the d = 2, 3 cases. Our method enables a study of circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the ϕ4 interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.

Black hole entropy in massive Type IIA

Abstract: We study the entropy of static dyonic BPS black holes in AdS4 in 4d gauged supergravities with vector and hyper multiplets, and how the entropy can be reproduced with a microscopic counting of states in the AdS/CFT dual field theory. We focus on the particular example of BPS black holes in AdS in massive Type IIA, whose dual three-dimensional boundary description is known and simple. To count the states in field theory we employ a supersymmetric topologically twisted index, which can be computed exactly with localization techniques. We find a perfect match at leading order.

Topological Complexity in AdS3/CFT2

Abstract: We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexityof a reduced density matrix is given by the spacetime volume contained inside theassociated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature.Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regionsand temperature. In particular, we find that the discontinuity that occurs under achange in the RT surface is given by a fixed topological contribution, independentof the temperature or details of the entangling region. We offer a definition andinterpretation of subregion complexity in the context of tensor networks, and shownumerically that it reproduces the qualitative features of the holographic computationin the case of a random tensor network using its relation to the Ising model. Finally,we give a prescription for computing subregion complexity directly in CFT using thekinematic space formalism, and use it to reproduce some of our explicit gravity resultsobtained at zero temperature. We thus obtain a concrete matching of results for subregioncomplexity between the gravity and tensor network approaches, as well as a CFT prescription.

T T ¯ $$ T\overline{T} $$ -deformations, AdS/CFT and correlation functions

Abstract: A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable $$ T\overline{T} $$ deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.

Evolution of complexity following a global quench

Abstract: The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a certain bulk region. We use ‘complexity equals action’ conjecture to study the time evolution of the complexity of the CFT state after a global quench. We find that the rate of growth of complexity is not only consistent with the conjectured bound, but it also saturates the bound soon after the system has achieved local equilibrium.

Strings with non-relativistic conformal symmetry and limits of the AdS/CFT correspondence

Abstract: We find a Polyakov-type action for strings moving in a torsional Newton-Cartan geometry. This is obtained by starting with the relativistic Polyakov action and fixing the momentum of the string along a non-compact null isometry. For a flat target space, we show that the world-sheet theory becomes the Gomis-Ooguri action. From a target space perspective these strings are non-relativistic but their world-sheet theories are still relativistic. We show that one can take a scaling limit in which also the world-sheet theory becomes non-relativistic with an infinite-dimensional symmetry algebra given by the Galilean conformal algebra. This scaling limit can be taken in the context of the AdS/CFT correspondence and we show that it is realized by the ‘Spin Matrix Theory’ limits of strings on AdS5 × S5. Spin Matrix theory arises as non-relativistic limits of the AdS/CFT correspondence close to BPS bounds. The duality between non-relativistic strings and Spin Matrix theory provides a holographic duality of its own and points towards a framework for more tractable holographic dualities whereby non-relativistic strings are dual to near BPS limits of the dual field theory.

Black hole elasticity and gapped transverse phonons in holography

Abstract: We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons — the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the translational symmetry breaking. These results provide a new confirmation that the BHs in these models do exhibit solid properties that become more manifest at low temperatures. Also, by the AdS/CFT correspondence, this allows to extend the standard results from the effective field theory for solids to quantum-critical materials.

Holographic complexity is nonlocal

Abstract: We study the “complexity equals volume” (CV) and “complexity equals action” (CA) conjectures by examining moments of of time symmetry for AdS3 wormholes having n asymptotic regions and arbitrary (orientable) internal topology. For either prescription, the complexity relative to n copies of the M = 0 BTZ black hole takes the form ΔC = αcχ, where c is the central charge and χ is the Euler character of the bulk time-symmetric surface. The coefficients α V = −4π/3, α A = 1/6 defined by CV and CA are independent of both temperature and any moduli controlling the geometry inside the black hole. Comparing with the known structure of dual CFT states in the hot wormhole limit, the temperature and moduli independence of α V , α A implies that any CFT gate set defining either complexity cannot be local. In particular, the complexity of an efficient quantum circuit building local thermofield-double-like entanglement of thermal-sized patches does not depend on the separation of the patches so entangled. We also comment on implications of the (positive) sign found for α A , which requires the associated complexity to decrease when handles are added to our wormhole.

5D rotating black holes and the nAdS2/nCFT1 correspondence

Abstract: We study rotating black holes in five dimensions using the nAdS2/nCFT1 correspondence. A consistent truncation of pure Einstein gravity (with a cosmological constant) in five dimensions to two dimensions gives a generalization of the Jackiw-Teitelboim theory that has two scalar fields: a dilaton and a squashing parameter that breaks spherical symmetry. The interplay between these two scalar fields is non trivial and leads to interesting new features. We study the holographic description of this theory and apply the results to the thermodynamics of the rotating black hole from a two dimensional point of view. This setup challenges notions of universality that have been advanced based on simpler models: we find that the mass gap of Kerr-AdS5 corresponds to an undetermined effective coupling in the nAdS2/nCFT1 theory which depends on ultraviolet data.

Holographic Spacetimes as Quantum Circuits of Path-Integrations

Abstract: We propose that holographic spacetimes can be regarded as collections of quantum circuits based on path-integrals We relate a codimension one surface in a gravity dual to a quantum circuit given by a path-integration on that surface with an appropriate UV cut off Our proposal naturally generalizes the conjectured duality between the AdS/CFT and tensor networks This largely strengthens the surface/state duality and also provides a holographic explanation of path-integral optimizations For static gravity duals, our new framework provides a derivation of the holographic complexity formula given by the gravity action on the WDW patch We also propose a new formula which relates numbers of quantum gates to surface areas, even including time-like surfaces, as a generalization of the holographic entanglement entropy formula We argue the time component of the metric in AdS emerges from the density of unitary quantum gates in the dual CFT Our proposal also provides a heuristic understanding how the gravitational force emerges from quantum circuits

Holographic Complexity of Einstein-Maxwell-Dilaton Gravity

Abstract: We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed “complexity = volume” and “complexity = action” dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, depending on the parameters of the theory, there is a parametric enhancement of the action growth rate relative to the conformal field theory result. We match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.

$$ J\overline{T} $$ deformed CFT2 and string theory

Abstract: We study two dimensional conformal field theory with a left-moving conserved current J, perturbed by an irrelevant, Lorentz symmetry breaking operator with the quantum numbers of $$ J\overline{T} $$ , using a combination of field and string theoretic techniques. Weshow that the spectrum of the theory has some interesting features, which may shed light on systems of interest for holography and black hole physics.

Chaotic Strings in AdS/CFT.

Abstract: Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos [J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106JHEPFG1029-847910.1007/JHEP08(2016)106]. It is interesting to ask whether this property is true only for leading large N correlators or if it can show up elsewhere. In this Letter, we consider the simplest setup to tackle this question: a Brownian particle coupled to a thermal ensemble. We find that the four-point out-of-time-order correlator that diagnoses chaos initially grows at an exponential rate that saturates the chaos bound, i.e., with a Lyapunov exponent λ_{L}=2π/β. However, the scrambling time is parametrically smaller than for plasma excitations, t_{*}∼βlogsqrt[λ] instead of t_{*}∼βlogN^{2}. Our result shows that, at least in certain cases, maximal chaos can be attained in the probe sector without the explicit need of gravitational degrees of freedom.