Schedule for: 21w5136 - Gravitational Emergence in AdS/CFT

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

I will describe a general statistical framework which seems to be able to capture many aspects of low-energy gravitational computations and naturally leads to e.g. ETH and averages of OPE coefficients

I will present a bulk reconstruction technique in AdS/CFT suitable for addressing a facet of the black hole information problem: how to unambiguously predict the results of measurements accessible to an infalling observer in the black hole interior.

The Schwarzschild wormhole has been interpreted as an entangled state. If Alice and Bob fall into each of the black hole, they can meet in the interior. We interpret this meeting in terms of the quantum circuit that prepares the entangled state. Alice and Bob create growing perturbations in the circuit, and we argue that the overlap of these perturbations represents their meeting. We identify the post-collision region as the region storing the gates that are not affected by any of the perturbations. We use this picture to analyze how the post-collision region shrinks after strong collisions between two localized shocks and compare it with estimated result from general relativity. We see that there is a boundary mechanism with which bulk matter gravitationally interact: perturbations overlapping in one shared quantum circuit. The same mechanism applies no matter the colliding signals come from the same boundary or different non-interacting boundaries.

We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining "areas" associated to arbitrary logical subsystems, and argue that this definition is "functionally unique." We also formalize a definition of bulk reconstruction that we call "state-specific product unitary" reconstruction. This definition captures the quantum error correction (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases. Our results extend to approximate codes, and even to the "non-isometric codes" that seem to describe the interior of a black hole at late times.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

I will show how to obtain entanglement negativity from replica wormholes in a couple of toy models of evaporating black holes. There are four phases dominated by different geometries. Some of these geometries are new replica wormholes that break the replica symmetry spontaneously. I will also show how to analyze the phase transitions and present enhanced corrections to negativity there.

A recipe for computing reflected entropy in random tensor networks is given, confirming the entanglement wedge cross section correspondence. We then discuss an effective description for the reflected entanglement spectrum that involves a sum over doubled tensor networks with an emergent area operator.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

This will be an overview of some paradigmatic inverse problems in Partial Differential Equations and Differential Geometry, some solved and some yet to be solved.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Evidence seems to suggest that semi-classical gravity computes the statistical distribution of the true microscopics of the dual CFT. In this talk, I will explore this idea for operator statistics. I will introduce the OPE Randomness Hypothesis (ORH), a generalization of the ETH ansatz to CFTs which is needed to describe the statistical properties of high energy states. I will provide evidence for the ORH conjecture and discuss the higher moments of OPE coefficients. The higher moments have implications for wormholes in the bulk dual, and seem to predict the existence of a new connected solution that dominates over the genus-2 wormhole.

In this talk we will consider the following question: Given any simple closed curve $\gamma$ on the boundary of a Riemannian 3-manifold $(M,g)$, suppose the area of the minimal surfaces bounded by $\gamma$ are known. From this data may we uniquely recover the metric $g$? For several cases, we show that the answer is yes. We will provide a global uniqueness result given area data for a much smaller class of curves on the boundary. The key to showing uniqueness for the metric $g$ is that we can reformulate parts of the problem as a 2-dimensional inverse problem on an area-minimizing surface. In particular, we relate least-area information to knowledge of the Dirichlet-to-Neumann map for the stability operator on a minimal surface. Broadly speaking, the question addressed is a codimension 1 version of the classical boundary rigidity problem for simply connected, Riemannian 3-manifolds with boundary, in which one seeks to determine $g$ given the distance between any two points on the boundary. We will briefly review this problem of boundary rigidity as it relates to aspects of our question of recovering $g$ from knowledge of areas. The results presented are joint work with S. Alexakis and A. Nachman.

The Covariant Entropy Bound implies a singularity in the domain of dependence of certain hyperentropic regions, i.e., regions whose entropy exceeds their boundary area. This extends the Penrose singularity theorem to a much larger class of surfaces. The quantum version of the bound implies a similar theorem in settings where quantum effects are dominant, such as a black hole after the Page time. This leads to an interesting puzzle: a singularity is predicted in a setting where the geometry appears to be smooth. (Work in progress with Arvin Shahbazi-Moghaddam.)

The black hole interior is a mysterious region of spacetime where non-perturbative effects are sometimes important. These non-perturbative effects are believed to be highly theory-dependent. In this work, we sharpen these statements by considering a setup where the state of the black hole is in a superposition of states corresponding to boundary theories with different couplings, entangled with a reference which keeps track of those couplings. We then ask for the entanglement wedge of the reference system, which we interpret as the region most sensitive to the values of the couplings. In simple bulk models, e.g., JT gravity $+$ a matter CFT, we use the QES formula to show that the reference contains the black hole interior at late times, and explicitly find the Renyi-2 wormhole that diagnoses the island. We also find numerical and analytical evidence of these statements in the SYK model. We argue that similar considerations are expected to apply in higher dimensional AdS/CFT, for marginal and even irrelevant couplings. (Work in progress with Ahmed Almheiri)

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

I will present recent progress on the following question: Consider a dynamical bulk space-time with a time-like boundary. Consider a wave equation on this bulk, and assume we know the following map: Create excitations for the wave on the boundary, and measure the resulting wave again at the boundary, where this excitation exits. (More precisely, consider The Dirichlet-to-Neumann map for this wave operator). Can one reconstruct the lower-order terms for the wave equation from this information? Can one hope to reconstruct the bulk metric from such measurements? I will present recent progress on this inverse problem, with particular emphasis on the links with the bulk geometry, and the behaviour of null geodesics therein. Joint work with Ali Feizmohammadi and Lauri Oksanen.

I discuss the relationship between the d-dimensional BCFT and CFT + gravity descriptions of double holography. In both formulations entropies in a bath region can be computed by the RT formula. I argue that the CFT + gravity description is analogous to semi-classical gravity if a different homology constraint for the RT formula is chosen and explore some consequences.

Euclidean wormholes are exotic types of gravitational solutions that we still don't understand completely. In the first part of the talk, I will analyze asymptotically AdS wormhole solutions from a gravitational point of view. By studying correlation functions of local and non-local operators, the universal properties that any putative holographic dual should exhibit, become manifest. In the second part, I will describe some concrete field theoretic models (both effective and microscopic) that share these properties.

The Kerr-Newman spacetime is the most general explicit black hole solution, and represents a stationary rotating charged black hole. Its stability to electromagnetic- gravitational perturbations has eluded a proof since the 80s in the black hole perturbation community, because of "the apparent indissolubility of the coupling between the spin-1 and spin-2 fields in the perturbed spacetime", as put by Chandrasekhar. We will present a derivation of the Teukolsky and Regge-Wheeler equations governing the perturbations of Kerr-Newman in physical space, and use it to obtain a quantitative proof of stability.

I will argue that novel (highly nonclassical) quantum extremal surfaces play a crucial role in reconstructing the black hole interior even for isolated, single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir). Specifically, any code subspace where interior outgoing modes can be excited will have a quantum extremal surface in its maximally mixed state. Therefore, the reconstruction of interior outgoing modes is always exponentially complex. As an application, I will show how these quantum extremal surfaces geometrize the exponential complexity of the black hole interior as discussed by Bouland, Fefferman, and Vazirani.

I will review the current status and future prospects for the black hole stability problem in general relativity and related problems, and discuss recent joint work with Holzegel, Rodnianski and Taylor (arXiv:2104.08222).

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

I consider an explicit example of a disordered holographic duality, where the average over an ensemble of free boson CFTs is dual to an exotic theory of gravity in AdS. This can be regarded as an explicit example of AdS/CFT duality, where all perturbative and non-perturbative effects can be computed exactly. For example, we can sum over Euclidean wormholes to obtain an exact formula for the two-point correlation function of the density of states. This wormhole sum reproduces precisely the late time "plateau" behaviour in the spectral form factor, which is related to discreteness of the spectrum. This leads to some interesting questions and speculations about the role of averaged holographic duality more generally.

I will focus on vacuum energy at zero and finite temperature in 1+2-dimensional holographic CFTs on curved spaces, and contrast it with that of free QFTs and CFTs. This energy for the holographic CFTs is determined by infilling bulk Einstein metrics with prescribed boundary data. I will discuss i) existence of such solutions, ii) some interesting constraints on the behaviour of vacuum energy following from existence of the bulk geometry, and iii) very surprising similarity in the detailed behaviour between holographic theories and free CFTs, particularly the free Dirac theory. A conjecture on the properties of certain heat kernels will also arise.

In 2007.07444, it was pointed out that wormholes do not only arise in the replica trick for the von Neumann entropy, but also in the gravitational path integral for extensive quantities like the (quenched) free energy. A replica trick computation of the free energy requires an analytic continuation to zero replicas which is not well understood and appears to be ambiguous. In this talk, I will present a general prescription inspired by Lewkowycz-Maldacena which disambiguates this trick by tracking gravitational saddle points in the continuum of replicas. I will then report on partial progress in applying this prescription to Jackiw-Teitelboim gravity coupled to conformal matter. (Based on work in progress with Ven Chandrasekaran, Netta Engelhardt and Sebastian Fischetti.)

Questions about quantum black holes have previously been sharpened by modelling them as a simple collection of qubits. Following this tradition, I introduce such a model which incorporates replica wormholes, and explain how small corrections to Hawking emission give rise to a Page curve in this model (evading a no-go result of Mathur).

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

We discuss aspects of the possible transition between small black holes and highly excited fundamental strings. We focus on the connection between black holes and the self gravitating string solution of Horowitz and Polchinski. This solution is interesting because it has non-zero entropy at the classical level and it is natural to suspect that it might be continuously connected to the black hole. Surprisingly, we find a different behavior for heterotic and type II cases. For the type II case we find an obstruction to the idea that the two are connected as classical solutions of string theory, while no such obstruction exists for the heterotic case. We further provide a linear sigma model analysis that suggests a continuous connection for the heterotic case. We also describe a solution generating transformation that produces a charged version of the self gravitating string. This provides a fuzzball-like construction of near extremal configurations carrying fundamental string momentum and winding charges. We provide formulas which are exact in α′ relating the thermodynamic properties of the charged and the uncharged solutions.

In this talk I will review recent work with Jie-qiang Wu, where we use the covariant "Peierls bracket" method to compute the algebra of many diffeormophism-invariant observables in JT gravity coupled to matter, and then use this algebra to re-derive (and clarify) many recent results. We also use it to study the complicated relationship between boundary energy and local rest-frame energy at different points in the vicinity of a horizon, which is of crucial importance to the "typical state" firewall paradox. Our methods naturally generalize to higher dimensions, where we do a few calculations as well, and our results suggest that the features of JT gravity extend in a fairly robust way.

Recent developments suggest that the sum over topologies in quantum gravity is related to an average over coupling constants, at least in certain models. I will describe an interacting toy model in 2d CFT where this can be studied in detail. The boundary theory is a WZW model averaged over exactly marginal deformations, and the bulk theory is a Chern-Simons-like theory in three dimensions.

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. This identification has many puzzles, including the boundary descriptions of the event horizons, the interiors of the black hole, and the singularities. Compounding these mysteries is the fact that, while there is no interaction between the CFTs, observers from them can fall into the black hole and interact. We will address these issues in this talk. In particular, we (i) present a boundary formulation of infalling observers; (ii) show that in any holographic systems, a sharp event horizon can only emerge in the infinite N limit; (iii) give an explicit construction in the boundary theory of an evolution operator for a bulk in-falling observer, making manifest the boundary emergence of the black hole horizons, the interiors, and the associated causal structure.

I show that the OPE between a light operator O_L and a heavy operator O_H in a 2d holographic CFT divides space into two regions, that can be identified with the exterior and interior of the dual black hole in AdS. Both the spatial geometry and gravitational red-shift factor can be derived from the CFT. Via this dictionary, the black hole information (or firewall) paradox arises as an apparent conflict between two ways of decomposing the four point function < O_H | O_L O_L | O_H > into conformal blocks. I explain how the crossing relation of the CFT resolves the paradox by means of an entanglement swap.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.