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.
We revisit the study of the probe scalar quasinormal modes of a class of three-charge supersymmetric microstate geometries. We compute the real and imaginary parts of the quasinormal modes and show that in the parameter range when the geometries have large AdS region, the spectrum is precisely reproduced from a D1-D5 orbifold CFT analysis. The spectrum includes the slow decaying modes pointed out by Eperon, Reall, and Santos. We analyse in detail the nature of the quasinormal modes by studying the scalar wavefunction. We show that these modes correspond to slow leakage of excitation from AdS t…
We construct an eternal traversable wormhole connecting two asymptotically $\text{AdS}_4$ regions. The wormhole is dual to the ground state of a system of two identical holographic CFT's coupled via a single low-dimension operator. The coupling between the two CFT's leads to negative null energy in the bulk, which supports a static traversable wormhole. As the ground state of a simple Hamiltonian, it may be possible to make these wormholes in the lab or on a quantum computer.
Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of …
In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems.…
We present the complete family of solutions of 3D gravity (Lambda<0) with two asymptotically AdS exterior regions. The solutions are constructed from data at the two boundaries, which correspond to two independent and arbitrary stress tensors T_R, \bar T_R, and T_L, \bar T_L. The two exteriors are smoothly joined on to an interior region through a regular horizon. We find CFT duals of these geometries which are entangled states of two CFT's. We compute correlators between general operators at the two boundaries and find perfect agreement between CFT and bulk calculations. We calculate and matc…
We study information theoretic properties of planar black hole microstates in 2 + 1 dimensional asymptotically anti-de Sitter spacetime, modeled by black holes with an end-of-the-world brane behind the horizon. The von Neumann entropy of sufficiently large subregions in the dual CFT exhibits a time-dependent phase, which from a doubly-holographic perspective corresponds to the appearance of quantum extremal islands in the brane description. Considering the case where dilaton gravity is added to the brane, we show that tuning the associated couplings affects the propagation of information in th…
We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying the null energy condition and having two asymptotically AdS boundaries connected through a (non-traversable) inflating wormhole. As for other wormholes, it is natural to expect dual descriptions in terms of two disconnected CFTs in appropriate entangled states. But for our cases certain expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT) prescription to compute CFT entropy do not exist. In particular, no real codimension-2 extremal surface can run from one end of the wormhole to the other.…
We use the Holevo information in a two-dimensional conformal field theory (CFT) with a large central charge $c$ to distinguish microstates from the underlying thermal state. Holographically, the CFT microstates of a thermal state are dual to black hole microstate geometries in three-dimensional anti-de Sitter space. It was found recently that the holographic Holevo information shows plateau behaviors at both short and long interval regions. This indicates that the black hole microstates are indistinguishable from the thermal state by measuring over a small region, and perfectly distinguishable…
For two-dimensional holographic CFTs, we demonstrate the role of Berry phases for relating the non-factorization of the Hilbert space to the presence of wormholes. The wormholes are characterized by a non-exact symplectic form that gives rise to the Berry phase. For wormholes connecting two spacelike regions in gravitational spacetimes, we find that the non-exactness is linked to a variable appearing in the phase space of the boundary CFT. This variable corresponds to a loop integral in the bulk. Through this loop integral, non-factorization becomes apparent in the dual entangled CFTs. Further…
A fundamental issue in the AdS/CFT correspondence is the wormhole growth paradox. Susskind's conjectured resolution of the paradox was to equate the volume of the wormhole with the circuit complexity of its dual quantum state in the CFT. We study the ramifications of this conjecture from a complexity-theoretic perspective. Specifically we give evidence for the existence of computationally pseudorandom states in the CFT, and argue that wormhole volume is measureable in a non-physical but computational sense, by amalgamating the experiences of multiple observers in the wormhole. In other words t…
We interpret the traversable wormhole in AdS/CFT in the context of quantum information theory. In particular, we investigate its properties as both a quantum channel and entanglement witness. We define protocols that allow either the bounding of the channel's entanglement capacity or the determination of aspects of the entanglement structure between the two boundary CFTs. Such protocols and connections allow for the use of quantum channel techniques in the study of gravitational physics and vice versa. More generally, our results suggest a purely quantum information-theoretic criterion for rec…
The holographic duals of Entanglement of Purification through the Entanglement Wedge Cross Section has been a well-discussed topic in the literature recently. More general entanglement measures involving multipartite information and their holographic duals have also been proposed. On the other hand, the recent intriguing program reproducing the Page Curve in Black hole entropy using the notion of islands has also been an obvious issue of attraction. A toy model involving Multiboundary wormholes in AdS$_{3}$ was able to capture many interesting facts about such calculations. In such a toy model…
We compute the full asymptotic symmetry group of black holes belonging to the same equivalence class of solutions within the Conformal Weyl Gravity formalism. We do this within an $AdS_2/CFT_1$ correspondence and by performing a Robinson-Wilczek two dimensional reduction, thus enabling the construction of an effective quantum theory of the remaining field content. The resulting energy momentum tensors generate asymptotic Virasoro algebras, to $s$-wave, with calculable central extensions. These centers in conjunction with their proper regularized lowest Virasoro eigen-modes yield the Bekenstein…
In the action-complexity proposal there are two different methods to regularize the gravitational on-shell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them for a pure BTZ black hole microstate. The microstate is obtained from a two-sided BTZ black hole truncated by a dynamical timelike ETW brane. Moreover, it is dual to a finite energy pure state in a two-dimensional CFT. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the Gibbons-Hawking-York term on the timelike boundary…
We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form ${\cal O} \widetilde{\cal O}$, where $\widetilde{\cal O}$ denote the state-dependent "mirror operators". We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to ty…
I present an informal overview of several recent results about Euclidean saddle points sourced by axion fields in quantum gravity (AdS/CFT), such as wormholes, their extremal "D-instanton" limits and their under-extremal singular counterparts. Concerning wormholes we argue they cannot contribute to the path integral because a stability analysis suggests they fragment like other super-extremal objects. For concrete AdS/CFT embeddings the Euclidean saddle point solutions are neatly described by geodesic curves living inside moduli spaces and can typically be solved for using group theory. Our wo…
Attempts to find black hole microstates using the Hamiltonian phase space approach have been made on the Schwarzschild spacetime. Since the Schwarzschild spacetime is also in the larger family of the Kerr spacetimes, and both are asymptotically flat, the Kerr black hole is a good option for the method development. The Kerr black hole is a spinning one. We perform this analysis on the Kerr spacetime and we obtain promising results using the covariant phase space analysis. Although we have forced ourselves to use the Bondi fall-off conditions, we find the gauge degrees of freedom that could be g…
The D1-D5 system has an orbifold point in its moduli space, at which it may be described by an ${\cal N} = (4,4)$ supersymmetric sigma model with target space $M^N/S(N)$ where $M$ is $\mathbb{T}^4$ or $K3$. In this paper we consider correlation functions involving chiral operators constructed from twist fields: we find explicit expressions for processes involving a twist $n$ operator joining $n$ twist operators of arbitrary twist. These expressions are universal, in that they are independent of the choice of $M$, and the final results can be expressed in a compact form. We explain how these re…
Typical black hole microstates in AdS/CFT were recently conjectured to have a geometrical dual with a smooth horizon and a portion of a second asymptotic region. I consider the application of the holographic complexity conjectures to this geometry. The holographic calculation leads to divergent values for the complexity; I argue that this classical divergence is consistent with expectations for typical microstates.
We obtain microstates accounting for the Gibbons-Hawking entropy in $dS_3$, along with a subleading logarithmic correction, from the solvable $T\bar T+Λ_2$ deformation of a seed CFT with sparse light spectrum. The microstates arise as the dressed CFT states near dimension $Δ=c/6$, associated with the Hawking-Page transition; they dominate the real spectrum of the deformed theory. We exhibit an analogue of the Hawking-Page transition in de Sitter. Appropriate generalizations of the $T\bar T+Λ_2$ deformation are required to treat model-dependent local bulk physics (subleading at large central ch…
We use Euclidean path integrals to explore the set of bulk asymptotically AdS spacetimes with good CFT duals. We consider simple bottom-up models of bulk physics defined by Einstein-Hilbert gravity coupled to thin domain walls and restrict to solutions with spherical symmetry. The cosmological constant is allowed to change across the domain wall, modeling more complicated Einstein-scalar systems where the scalar potential has multiple minima. In particular, the cosmological constant can become positive in the interior. However, in the above context, we show that inflating bubbles are never pro…
We reconsider the role of wormholes in the AdS/CFT correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with $\mathbb{S}^1\times \mathbb{S}^{d-1}$ boundary. There is no solution to Einstein's equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constr…
Inspired by the recent work of Bao and Ooguri (BO), we study the distinguishability of the black hole microstates from the thermal state as captured by the average of their relative entropies: the Holevo information. Under the assumption that the vacuum conformal block dominates the entropy calculation, BO find that the average relative entropy vanishes on spatial regions less than half the size of the CFT. However, vacuum block dominance fails for some microstates of the $M=0$ BTZ black hole. We show that this renders the average relative entropy nonzero even on infinitesimal intervals at $O(…
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bu…
We compute one point functions of chiral primary operators in the D1-D5 orbifold CFT, in classes of states corresponding to microstates of two and three charge black holes. Black hole microstates describable by supergravity solutions correspond to coherent superpositions of states in the orbifold theory and we develop methods for approximating one point functions in such superpositions in the large N limit. We show that microstates built from long strings (large twist operators) have one point functions that are suppressed by powers of N. Accordingly, even when these microstates admit supergra…
We analyze the 1+1 CFT states dual to hot (time-symmetric) 2+1 multiboundary AdS wormholes. These are black hole geometries with high local temperature, $n \ge 1$ asymptotically-AdS$_3$ regions, and arbitrary internal topology. The dual state at $t=0$ is defined on $n$ circles. We show these to be well-described by sewing together tensor networks corresponding to thermofield double states. As a result, the entanglement is spatially localized and bipartite: away from particular boundary points ("vertices") any small connected region $A$ of the boundary CFT is entangled only with another small c…
We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS$_3$/CFT$_2$. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS$_3$ higher spin gravity. The fixed spin sectors of the dual CFT$_2$ exhibit features that starkly go beyond conventional random matrix ensembles: power-law ramps in the spectral form factor and potentials with a double-well/crest underlying the level statistics.
This paper revisits the question of reconstructing bulk gauge fields as boundary operators in AdS/CFT. In the presence of the wormhole dual to the thermofield double state of two CFTs, the existence of bulk gauge fields is in some tension with the microscopic tensor factorization of the Hilbert space. I explain how this tension can be resolved by splitting the gauge field into charged constituents, and I argue that this leads to a new argument for the "principle of completeness", which states that the charge lattice of a gauge theory coupled to gravity must be fully populated. I also claim tha…
Recently it was proposed that microscopic models of braneworld cosmology could be realized in the context of AdS/CFT using black hole microstates containing an end-of-the-world brane. Motivated by a desire to establish the microscopic existence of such microstates, which so far have been discussed primarily in bottom-up models, we have studied similar microstates in a simpler version of AdS/CFT. On one side, we define and study boundary states in the charged Sachdev-Ye-Kitaev model and show that these states typically look thermal with a certain pattern of symmetry breaking. On the other side,…
Gravitational wave observations of the near-horizon region of black holes lend insight into the quantum nature of gravity. In particular, gravitational wave echoes have been identified as a potential signature of quantum gravity-inspired structure near the horizon. In this paper, we connect such observables to the language of black hole microstates in string theory and holography. To that end, we propose a toy model describing the AdS$_3$ near-horizon region of five-dimensional black holes, inspired by earlier work of Solodukhin. This model captures key features of recently constructed microst…
We attempt to construct eternal traversable wormholes connecting two asymptotically AdS regions by introducing a static coupling between their dual CFTs. We prove that there are no semiclassical traversable wormholes with Poincaré invariance in the boundary directions in higher than two spacetime dimensions. We critically examine the possibility of evading our result by coupling a large number of bulk fields. Static, traversable wormholes with less symmetry may be possible, and could be constructed using the ingredients we develop here.
Recent studies of asymptotic symmetries suggest, that a Hamiltonian phase space analysis in gravitational theories might be able to account for black hole microstates. In this context we explain, why the use of conventional Bondi fall-off conditions for the gravitational field is too restrictive in the presence of an event horizon. This implies an enhancement of physical degrees of freedom ($\mathcal{A}$-modes). They provide new gravitational hair and are responsible for black hole microstates. Using covariant phase space methods, for the example of a Schwarzschild black hole, we give a propos…
Certain closed-universe big-bang/big-crunch cosmological spacetimes may be obtained by analytic continuation from asymptotically AdS Euclidean wormholes, as emphasized by Maldacena and Maoz. We investigate how these Euclidean wormhole spacetimes and their associated cosmological physics might be described within the context of AdS/CFT. We point out that a holographic model for cosmology proposed recently in arXiv:1810.10601 can be understood as a specific example of this picture. Based on this example, we suggest key features that should be present in more general examples of this approach to …
