We reinterpret the OSV formula for the on-shell action/entropy function of asymptotically flat BPS black holes as a fixed point formula that is formally equivalent to a recent gluing proposal for asymptotically $\operatorname{AdS}_4$ black holes. This prompts a conjecture that the complete perturbative answer for the most general gravitational building block of 4d $N = 2$ supergravity at a single fixed point takes the form of a Nekrasov-like partition function with equivariant parameters related to the higher-derivative expansion of the prepotential. In turn this leads to a simple localization-like proposal for a set of supersymmetric partition functions in (UV completed) 4d $N = 2$ supergravity theories. The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. In particular, it follows that the OSV formula comes from the unrefined limit of the general expression including only the so-called $\mathbb{W}$ tower of higher derivatives, while the on-shell action of pure (Euclidean) $\operatorname{AdS}_4$ with round $S^3$ boundary comes from the NS limit that includes only the $\mathbb{T}$ tower.

We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields with large central charge in the presence of the black hole, including the backreaction corrections to the BTZ metric. Our results show that Volume Complexity admits a consistent quantum expansion and correctly reproduces known limits. On the other hand, the generalized Action Complexity fails to account for the additional contributions from bulk quantum fields and does not lead to the correct classical limit. Furthermore, we show that the doubly-holographic setup allows computing the complexity coming purely from quantum fields - a notion that has proven evasive in usual holographic setups. We find that in holographic induced-gravity scenarios the complexity of quantum fields in a black hole background vanishes to leading order in the gravitational strength of CFT effects.

Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from "nearby" theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

The holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to $n=5$ regions. I explain that average entropies of $p$-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions $n$. This analysis defines the Holographic Cone of Average Entropies (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

We study the spectral statistics of primary operators in the recently formulated ensemble average of Narain's family of free boson conformal field theories, which provides an explicit (though exotic) example of an averaged holographic duality. In particular we study moments of the partition function by explicit computation of higher-degree Eisenstein series. This describes the analog of wormhole contributions coming from a sum of over geometries in the dual theory of "$U(1)$ gravity" in $\operatorname{AdS}_3$. We give an exact formula for the two-point correlation function of the density of primary states. We compute the spectral form factor and show that the wormhole sum reproduces precisely the late time plateau behaviour related to the discreteness of the spectrum. The spectral form factor does not exhibit a linear ramp.

We discuss generalizations of the TFD to a density matrix on the doubled Hilbert space. We suggest that a semiclassical wormhole corresponds to a certain class of such density matrices, and specify how they are constructed. Different semi-classical profiles correspond to different non-overlapping density matrices. We show that this language allows for a finer criteria for when the wormhole is semiclassical, which goes beyond entanglement. Our main tool is the SYK model. We focus on the simplest class of such density matrices, in a scaling limit where the ER bridge is captured by chords going from one space to another, encoding correlations in the microscopic Hamiltonian. The length of the wormhole simply encodes the extent these correlations are eroded when flowing from one side to the other.

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. Furthermore, we classify Berry phases in holographic CFTs based on the type of dual bulk diffeomorphism involved and show that each type of Berry phase corresponds to a spacetime wormhole geometry in the bulk.

All known horizonless black-hole microstate geometries correspond to brane sources that acquire a finite size, and hence break the spherical symmetry of the black hole. We construct, for the first time, solutions with zero horizon area that have the same charges as a three-charge F1-NS5-P Type-IIA black hole and preserve this spherical symmetry. The momentum of these solutions is carried by longitudinal D0-D4 density fluctuations inside the NS5-branes. We argue that these solutions should be interpreted as the long-throat limit of a family of smooth, horizonless microstate geometries, called superstrata, where such geometries degenerate. The existence of these geometries indicates that a finite-size horizon does not appear even in the singular corners of the moduli space of three-charge microstate geometries.

We study the semi-classical thermodynamics of two-dimensional de Sitter space ($\operatorname{dS}_2$) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of Brown and York to $\operatorname{dS}_2$, where a timelike boundary is introduced in the static patch to uniquely define conserved charges, including quasi-local energy. The boundary divides the static patch into two systems, a cosmological system and a black hole system, the former being unstable under thermal fluctuations while the latter is stable. A semi-classical quasi-local first law is derived, where the Gibbons–Hawking entropy is replaced by the generalized entropy. In the microcanonical ensemble the generalized entropy is stationary. Further, we show the on-shell Euclidean microcanonical action of a causal diamond in semi-classical JT gravity equals minus the generalized entropy of the diamond, hence extremization of the entropy follows from minimizing the action. Thus, we provide a first principles derivation of the island rule for $U(1)$ symmetric $\operatorname{dS}_2$ backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.

The island formula – an extremization prescription for generalized entropy – is known to result in a unitary Page curve for the entropy of Hawking radiation. This semi-classical entropy formula has been derived for Jackiw-Teitelboim (JT) gravity coupled to conformal matter using the “replica trick” to evaluate the Euclidean path integral. Alternatively, for eternal Anti-de Sitter black holes, we derive the extremization of generalized entropy from minimizing the microcanonical action of an entanglement wedge. The on-shell action is minus the entropy and arises in the saddle-point approximation of the (nonreplicated) microcanonical path integral. When the black hole is coupled to a bath, islands emerge from maximizing the entropy at fixed energy, consistent with the island formula. Our method applies to JT gravity as well as other two-dimensional dilaton gravity theories.

I will describe the constraints due to modularity on the spectrum of two-dimensional SCFTs arising from compactification of M5 branes on divisors in one-parameter compact Calabi-Yau threefolds. These constraints are strong enough to determine the torus partition function (given by vector-valued modular forms for unit magnetic M5 charge) in terms of the polar terms. Consequently, our ansatz for the vector valued modular forms allows us to predict an infinite series of Donaldson-Thomas invariants associated with the target Calabi-Yau manifold. I will conclude with some comments on the exceptional cases of Calabi-Yau manifolds for which our ansatz fails, and on the cases with multiple M5 branes.

Based on work (2204.02207) in collaboration with Sergei Alexandrov, Jan Manschot, and Boris Pioline.

We develop a model of one-dimensional (Conformal) Quantum Gravity. By discussing the connection between Goldstone and Gauge theories, we establish that this model effectively computes the partition function of the Schwarzian theory where the $\operatorname{SL}(2,\mathbb{R})$ symmetry is realized on the base space. The computation is straightforward, involves a local quantum measure and does not rely on localization arguments. Non-localities in the model are exclusively related to the value of fixed gauge invariant moduli. Furthermore, we study the properties of these models when all degrees of freedom are allowed to fluctuate. We discuss the UV finiteness properties of these systems and the emergence of a Planck's length.

We present a new infinite class of gravitational observables in asymptotically Anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switch-back effect in shock wave geometries. We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.

Diffeomorphism symmetry is an intrinsic difficulty in gravitational theory, which appears in almost all of the questions in gravity. As is well known, the diffeomorphism symmetries in gravity should be interpreted as gauge symmetries, so only diffeomorphism invariant operators are physically interesting. However, because of the non-linear effect of gravitational theory, the results for diffeomorphism invariant operators are very limited.

In this work, we focus on the Jackiw-Teitelboim gravity in classical limit, and use Peierls bracket (which is a linear response like computation of observables’ bracket) to compute the algebra of a large class of diffeomorphism invariant observables. With this algebra, we can reproduce some recent results in Jackiw-Teitelboim gravity including: traversable wormhole, scrambling effect, and $SL(2)$ charges. We can also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the “typical state” version of the firewall paradox.

In the talk, I will first give a brief introduction of Peierls bracket, and then use the Peierls bracket to study the brackets between diffeomorphism invariant observables in Jackiw-Teitelboim gravity. I will then give two applications of this algebra: reproducing the scrambling effect, and studying the energy change after creating an excitation in the bulk.

Work based on https://arxiv.org/pdf/2108.04841.pdf

Recent developments involving replica wormholes, the generalized entropy, quantum extremal surfaces, holographic map, etc, have shown what is missing in Hawking’s original calculation. We can now see how to perform semi-classical calculations that are entirely consistent with unitary: information is not lost. The state of the Hawking radiation has subtle correlations that build up as a black hole evaporates and ensure that the final state is pure. The interpretation of the results for the picture of a black hole with a smooth internal geometry before the singularity is reached is less clear. I will review these developments and present a simple microscopic model which can be used to illustrate the issues involved. The recent observation that the holographic map, the map between the semi-classical and microscopic states, is non-isometric plays a key role. Contrary to some suggestions, manipulation of the radiation far from the black hole cannot affect its interior in a non-local way. The picture seems entirely consistent with microscopic constructions like fuzzballs in string theory.

I will first motivate the benefits on taking the algebraic approach to understand AdS/CFT and how an algebra of local operators of QFT has knowledge of a spacetime region. Utilizing both operator algebras and quantum information theory, I will explain a new framework for understanding nonperturbative gravitational aspects of bulk reconstruction with a finite or infinite-dimensional boundary Hilbert space. This will be understood as approximate recovery containing gravitational errors, and the bulk reconstruction in this context will be understood using the privacy/correctability correspondence.