Showing papers on "AdS/CFT correspondence published in 2021"

Symmetries in Quantum Field Theory and Quantum Gravity

Abstract: In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any “long-range” bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the “convex hull condition” of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and ’t Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman–Mandula theorem to discrete symmetries, and an improved explanation of the decay $$\pi ^0\rightarrow \gamma \gamma $$ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in $$d+1$$ dimensions with horizon topology $${\mathbb {T}}^p\times {\mathbb {S}}^{d-p-1}$$ .

Free partition functions and an averaged holographic duality

Abstract: 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 ×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Island in the Presence of Higher Derivative Terms

Abstract: Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary

AdS 3 gravity and random CFT

Abstract: We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.

Quantum extremal islands made easy. Part III. Complexity on the brane

Abstract: We examine holographic complexity in the doubly holographic model introduced in [1, 2] to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the brane. Motivated by these results, we propose a generalization of the CV proposal for higher curvature theories of gravity. Further, we provide two consistency checks of our proposal by studying Gauss-Bonnet gravity and f(ℛ) gravity in the bulk.

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

Abstract: We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in d-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

Evaporating black holes coupled to a thermal bath

Abstract: We study the doubly holographic model of [1] in the situation where a black hole in two-dimensional JT gravity theory is coupled to an auxiliary bath system at arbitrary finite temperature. Depending on the initial temperature of the black hole relative to the bath temperature, the black hole can lose mass by emitting Hawking radiation, stay in equilibrium with the bath or gain mass by absorbing thermal radiation from the bath. In all of these scenarios, a unitary Page curve is obtained by applying the usual prescription for holographic entanglement entropy and identifying the quantum extremal surface for the generalized entropy, using both analytical and numeric calculations. As the application of the entanglement wedge reconstruction, we further investigate the reconstruction of the black hole interior from a subsystem containing the Hawking radiation. We examine the roles of the Hawking radiation and also the purification of the thermal bath in this reconstruction.

Color/kinematics duality in AdS 4

Abstract: In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ relations for Yang-Mills amplitudes and underlies the double copy to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills amplitudes in AdS4. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit. We illustrate these results using compact new expressions for 4-point Yang-Mills amplitudes in AdS4 and their kinematic numerators in terms of spinors. We also spell out the relation to 3d conformal correlators in momentum space, and speculate on the double copy to graviton amplitudes in AdS4.

Islands and Page curves of Reissner-Nordström black holes

Abstract: We apply the recently proposed quantum extremal surface construction to calculate the Page curve of the eternal Reissner-Nordstrom black holes in four dimensions ignoring the backreaction and the greybody factor. Without the island, the entropy of Hawking radiation grows linearly with time, which results in the information paradox for the eternal black holes. By extremizing the generalized entropy that allows the contributions from the island, we find that the island extends to the outside the horizon of the Reissner-Nordstrom black hole. When taking the effect of the islands into account, it is shown that the entanglement entropy of Hawking radiation at late times for a given region far from the black hole horizon reproduces the Bekenstein-Hawking entropy of the Reissner-Nordstrom black hole with an additional term representing the effect of the matter fields. The result is consistent with the finiteness of the entanglement entropy for the radiation from an eternal black hole. This facilitates to address the black hole information paradox issue in the current case under the above-mentioned approximations.

BCFT entanglement entropy at large central charge and the black hole interior

Abstract: In this note, we consider entanglement and Renyi entropies for spatial subsystems of a boundary conformal field theory (BCFT) or of a CFT in a state constructed using a Euclidean BCFT path integral. Holographic calculations suggest that these entropies undergo phase transitions as a function of time or parameters describing the subsystem; these arise from a change in topology of the RT surface. In recent applications to black hole physics, such transitions have been seen to govern whether or not the bulk entanglement wedge of a (B)CFT region includes a portion of the black hole interior and have played a crucial role in understanding the semiclassical origin of the Page curve for evaporating black holes. In this paper, we reproduce these holographic results via direct (B)CFT calculations. Using the replica method, the entropies are related to correlation functions of twist operators in a Euclidean BCFT. These correlations functions can be expanded in various channels involving intermediate bulk or boundary operators. Under certain sparseness conditions on the spectrum and OPE coefficients of bulk and boundary operators, we show that the twist correlators are dominated by the vacuum block in a single channel, with the relevant channel depending on the position of the twists. These transitions between channels lead to the holographically observed phase transitions in entropies.

Geometric secret sharing in a model of Hawking radiation

Abstract: We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

A Basis of Analytic Functionals for CFTs in General Dimension

Abstract: We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis for this space of functions, consisting of the set of s- and t-channel conformal blocks of double-twist operators in mean field theory. We describe two independent algorithms to construct the dual basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and Caron-Huot.

The statistical mechanics of near-extremal black holes

Abstract: An important open question in black hole thermodynamics is about the existence of a “mass gap” between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordstrom near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on S2 in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of 2d Jackiw-Teitelboim gravity coupled to the electromagnetic U(1) gauge field and to an SO(3) gauge field generated by the dimensional reduction.

Islands and Page curves in 4d from Type IIB

Abstract: Variants of the black hole information paradox are studied in Type IIB string theory setups that realize four-dimensional gravity coupled to a bath. The setups are string theory versions of doubly-holographic Karch/Randall brane worlds, with black holes coupled to non-gravitating and gravitating baths. The 10d versions are based on fully backreacted solutions for configurations of D3, D5 and NS5 branes, and admit dual descriptions as $$ \mathcal{N} $$ = 4 SYM on a half space and 3d $$ {T}_{\rho}^{\sigma } $$ [SU(N)] SCFTs. Island contributions to the entanglement entropy of black hole radiation systems are identified through Ryu/Takayanagi surfaces and lead to Page curves. Analogs of the critical angles found in the Karch/Randall models are identified in 10d, as critical parameters in the brane configurations and dual field theories.

Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

Abstract: We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincare patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

Island in Charged Black Holes

Abstract: We study the information paradox for the eternal black hole with charges on a doubly-holographic model in general dimensions, where the charged black hole on a Planck brane is coupled to the baths on the conformal boundaries. In the case of weak tension, the brane can be treated as a probe such that its backreaction to the bulk is negligible. We analytically calculate the entanglement entropy of the radiation and obtain the Page curve with the presence of an island on the brane. For the near-extremal black holes, the growth rate is linear in the temperature. Taking both Dvali-Gabadadze-Porrati term and nonzero tension into account, we obtain the numerical solution with backreaction in four-dimensional spacetime and find the quantum extremal surface at t = 0. To guarantee that a Page curve can be obtained in general cases, we propose two strategies to impose enough degrees of freedom on the brane such that the black hole information paradox can be properly described by the doubly-holographic setup.

Defect extremal surface as the holographic counterpart of Island formula

Abstract: We propose defect extremal surface as the holographic counterpart of boundary quantum extremal surface. The defect extremal surface is defined by minimizing the Ryu-Takayanagi surface corrected by the defect theory. This is particularly interesting when the RT surface crosses or terminates on the defect. In a simple set up of AdS/BCFT, we find that the defect extremal surface formula gives precisely the same results of the boundary quantum extremal surface. We provide a decomposition procedure of an AdS bulk with a defect brane to see clearly how quantum extremal surface formula emerges from a brane world system with gravity glued to a flat space quantum field theory.

Signatures of global symmetry violation in relative entropies and replica wormholes

Abstract: It is widely believed that exact global symmetries do not exist in theories that admit quantum black holes. Here we propose a way to quantify the degree of global symmetry violation in the Hawking radiation of a black hole by using certain relative entropies. While the violations of global symmetry that we consider are non-perturbative effects, they nevertheless give $$ \mathcal{O} $$ (1) contributions to the relative entropy after the Page time. Furthermore, using “island” formulas, these relative entropies can be computed within semi-classical gravity, which we demonstrate with explicit examples. These formulas give a rather precise operational sense to the statement that a global charge thrown into an old black hole will be lost after a scrambling time. The relative entropies considered here may also be computed using a replica trick. At integer replica index, the global symmetry violating effects manifest themselves as charge flowing through the replica wormhole.

On duality of color and kinematics in (A)dS momentum space

Abstract: We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS4 and the second for the integrand in general AdSd+1. For the integrated correlator, we find color-kinematics does not yield additional relations among n-point, color-ordered correlators. To study color-kinematics for the AdSd+1 Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−1 and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

On genus-one string amplitudes on AdS 5 × S 5

Abstract: We study non-planar correlators in $$ \mathcal{N} $$ = 4 super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order 1/N4 and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on AdS5 × S5 in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.

A derivation of AdS/CFT for vector models

Abstract: We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev’s classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.

Classifying boundary conditions in JT gravity: from energy-branes to α-branes

Abstract: We classify the possible boundary conditions in JT gravity and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties and ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and, finally, its role as a two-dimensional model of cosmology.

Summing over geometries in string theory

Abstract: We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions We discuss this problem with the help of the tensionless string on $$ {\mathrm{\mathcal{M}}}_3\times {\mathrm{S}}^3\times {\mathbbm{T}}^4 $$ (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold SymN ( $$ {\mathbbm{T}}^4 $$ ) We strengthen the analysis of [1] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ3 We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕N SymN ( $$ {\mathbbm{T}}^4 $$ ) The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’ We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries We also briefly discuss the effect of ensemble averaging over the Narain moduli space of $$ {\mathbbm{T}}^4 $$ and of deforming away from the orbifold by the marginal deformation

Free field world-sheet correlators for AdS3

Abstract: We employ the free field realisation of the $$ \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 $$ world-sheet theory to constrain the correlators of string theory on AdS3 × S3 × 𝕋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 by the (genus zero) world-sheet — this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable ‘incidence relation’ obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.

Unitarity of entanglement and islands in two-sided Janus black holes

Abstract: We explore the entanglement evolution of boundary intervals in eternal Janus black holes that can be embedded consistently into string theory in the low-energy limit. By studying the geodesics we show that there is a transition in the entanglement characteristic around the Page time, which manifests the unitarity of the evolution. We reproduce and reinterpret these bulk results from two different lower-dimensional perspectives: first as an interface CFT in the usual AdS/CFT correspondence and second as an effective gravity theory in one lower dimension coupled to a radiation background. In the limit where the number of interface degrees of freedom becomes large, we obtain an effective theory on appropriate branes that replace the deep interior region in the bulk, coined the shadow region. In this effective theory, we also identify the island of the radiation entanglement wedge and verify the newly proposed quantum extremization method. Our model clarifies that double holography with gravity in two higher dimensions can be realized in a concrete and consistent way and that the occurrence of islands is natural in one higher dimension. Furthermore, our model reveals that there can be a transitional behavior of the Page curve before the Page time, which is related to the emergence of new matter degrees of freedom on the branes.

Complexity growth of operators in the SYK model and in JT gravity

Abstract: The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.

6d (2, 0) and M-theory at 1-loop

Abstract: We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric (2, 0) AN−1 and DN theories, which have no Lagrangian description, but in the large N limit are holographically dual to weakly coupled M-theory on AdS7 × S4 and AdS7 × S4/ℤ2, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

Partition functions of the tensionless string

Abstract: We consider string theory on AdS3 × S3 × 𝕋4 in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal AdS3, the BTZ black hole, conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on thermal AdS3 and the conical defect with a torus boundary is shown to agree, thus giving evidence for the equivalence of the tensionless string on these different background geometries. We also find that thermal AdS3 and the BTZ black hole are dual descriptions and the vacuum of the BTZ black hole is mapped to a single long string winding many times asymptotically around thermal AdS3. Thus the system yields a concrete example of the string-black hole transition. Consequently, reproducing the boundary partition function does not require a sum over bulk geometries, but rather agrees with the string partition function on any bulk geometry with the appropriate boundary. We argue that the same mechanism can lead to a resolution of the factorization problem when geometries with disconnected boundaries are considered, since the connected and disconnected geometries give the same contribution and we do not have to include them separately.

Cosmological singularities, entanglement and quantum extremal surfaces

Abstract: We study aspects of entanglement and extremal surfaces in various families of spacetimes exhibiting cosmological, Big-Crunch, singularities, in particular isotropic AdS Kasner. The classical extremal surface dips into the bulk radial and time directions. Explicitly analysing the extremization equations in the semiclassical region far from the singularity, we find the surface bends in the direction away from the singularity. In the 2-dim cosmologies obtained by dimensional reduction of these and other singularities, we have studied quantum extremal surfaces by extremizing the generalized entropy. The resulting extremization shows the quantum extremal surfaces to always be driven to the semiclassical region far from the singularity. We give some comments and speculations on our analysis.

Wormholes and black hole microstates in AdS/CFT

Abstract: It has long been known that the coarse-grained approximation to the black hole density of states can be computed using classical Euclidean gravity. In this work we argue for another entry in the dictionary between Euclidean gravity and black hole physics, namely that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates. To do so we use the method of constrained instantons to obtain an integral representation of wormhole amplitudes in Einstein gravity and in full-fledged AdS/CFT. These amplitudes are non-perturbative corrections to the two-boundary problem in AdS quantum gravity. The full amplitude is likely UV sensitive, dominated by small wormholes, but we show it admits an integral transformation with a macroscopic, weakly curved saddle-point approximation. The saddle is the "double cone" geometry of Saad, Shenker, and Stanford, with fixed moduli. In the boundary description this saddle appears to dominate a smeared version of the connected two-point function of the black hole density of states, and suggests level repulsion in the microstate spectrum. Using these methods we further study Euclidean wormholes in pure Einstein gravity and in IIB supergravity on Euclidean AdS$_5\times\mathbb{S}^5$. We address the perturbative stability of these backgrounds and study brane nucleation instabilities in 10d supergravity. In particular, brane nucleation instabilities of the Euclidean wormholes are lifted by the analytic continuation required to obtain the Lorentzian spectral form factor from gravity. Our results indicate a factorization paradox in AdS/CFT.