Abstracts

Nikolay Bobev: Large N Partition Functions, Holography, and Black Holes

I will discuss the large N behavior of partition functions of the ABJM theory on compact Euclidean manifolds. I will pay particular attention to the S^3 free energy and the topologically twisted index for which I will present closed form expressions valid to all order in the large N expansion. These results have important implications for holography and the microscopic entropy counting of AdS_4 black holes which I will discuss. I will also briefly discuss generalizations to other SCFTs arising from M2-branes.

Alejandra Castro: The stranger things of symmetric product orbifolds

I will discuss the large-N limit of two-dimensional symmetric product orbifolds. The goal is to single out which symmetric product orbifold theory could lead to a strongly coupled point in their moduli space, whose dual could be a semi-classical theory of AdS_3 gravity. To this end, we consider the symmetric product orbifold of tensor products of N=2 super-Virasoro minimal models, and classify them according to two criteria. The first criterion is the existence of a single-trace twisted exactly marginal operator in their moduli space. The second criterion is a sparseness condition on the growth of light states in the elliptic genera. In this context, we encounter a strange variety: theories that obey the first criterion but the second criterion falls into a Hagedorn-like growth. I will explain why this may be counter-intuitive and discuss how it might be accounted for in conformal perturbation theory. I will also present a new infinite class of theories that obey both criteria, which are necessary conditions for their moduli spaces to contain a supergravity point.

Ben Craps: Bounds on quantum evolution complexity via lattice cryptography

We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate `complexity metric' must be used that takes into account the relative difficulty of performing `nonlocal' operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to ~10^4.

Sumit R. Das: Target space entanglement and holography

Entanglement between regions of the base space of a holographic field theory is intimately tied to the emergence of a smooth bulk. This suggests that the emergence of internal spaces in the bulk is tied to entanglement in target space. We discuss how such a target space entanglement between matrix degrees of freedom can be defined in a gauge invariant fashion, and its implications to String Theory.

Thomas Faulkner: Asymptotically isometric codes for holography

I will discuss a new class of quantum error correcting codes that are defined by a sequence of theories. With some technical assumptions these codes can be derived from the large N limit of SU(N) gauge theories by focusing on single trace operators. We show that the resulting code subspace has many features in common with an emergent gravitational theory. This includes a notion of causal wedges and entanglement wedges associated to boundary regions. Non trivial von Neumann algebras can emerge as the local algebra of operators on the code subspace.

Victor Godet: The gravity dual of complexified SYK

The SYK model is a simple quantum mechanical theory which has an effective dual description in terms of JT gravity. It provides a solvable toy model of AdS/CFT which has already found numerous applications and led to many insights. In this talk we ask: what is the gravity dual of SYK with complexified couplings? We propose that it is JT gravity with complex sources for a massless scalar field. These boundary sources can be used to obtain wormhole and half-wormhole saddle points in the gravity path integral. Their distinctive effects can be seen in the free energy and matched with the microscopic SYK description. In this model, the factorization puzzle can be addressed and one can describe the gravity dual of SYK at a single realization of the couplings. After turning on a double trace deformation, we also observe a surprising complex-to-real phase transition in SYK, dual to a Euclidean-to-Lorentzian wormhole transition in JT gravity.

Tom Hartman: Wormholes and coarse graining in CFT

Euclidean wormholes play an essential role in black hole information, but they also lead to the factorization puzzle, seemingly in tension with quantum mechanics and AdS/CFT. This has led to the suggestion that wormholes arise from coarse graining over UV degrees of freedom. In this talk I will explain the puzzle, show that certain Euclidean wormholes in higher dimensions do have a coarse-grained interpretation, and in 3D gravity, relate this to averaging over approximate solutions of the 2D conformal bootstrap equations.

Lotte Hollands: Non-perturbative topological strings and 5d BPS states

Recently, a rather elegant picture has emerged for the non-perturbative topological string. In this picture the non-perturbative partition function has a piecewise-constant dependence on an additional phase, and jumps have an interpretation in terms of 5d BPS states. In this talk I will explain the details of this picture in the example of the resolved conifold, where the partition function may be obtained as a Borel sum, as well as its relation to an analogous picture for the Nekrasov-Rosly-Shatashvili superpotential for four-dimensional N=2 theories.

Albrecht Klemm: Calabi-Yau Manifolds, Modularity and Arithmetic Geometry

Using Mirror symmetry and Dworks p-adic deformation of the Gauss Manin connections we construct the Hasse Weil Zeta function of $\zeta(X/\mathbb{Q}, s)$ for families of Calabi-Yau threefolds $X$ and explore the consequences of its modularity in special fibres at algebraic extension of $\mathbb{Q}$ on the physics of string compactifications on $X$ as well as on enumerative geometry on $X$.

Wei Li: From BPS crystals to BPS algebras

I will explain how to construct BPS algebras for string theory on general toric Calabi-Yau threefolds, based on the crystal melting description of the BPS sectors. The resulting quiver Yangians, together with their trigonometric and elliptic versions, unify various known results and generalize them to a much larger class. I will then explain how to describe their representations using subcrystals and how they can be translated into the framings of the quivers. Finally, I will discuss some applications, such as how to use these algebras to count BPS states efficiently and how to use them to give an algebraic derivation of the Gauge/Bethe correspondence.

Dario Martelli: Gravitational Blocks, Spindles and GK Geometry

We derive a gravitational block formula for the supersymmetric action of a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$_3$ solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS$_2$ solutions of $D=11$ supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle.We develop geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and significantly generalizing these results to other compactifications. Our gravitational block formula agrees with various conjectural expressions in the literature, and extend those to a much broader class of solutions, including supersymmetric and accelerating black holes in AdS$_4$.

Samir Mathur: The nonperturbative structure of the quantum gravity vacuum

The traditional picture of the vacuum says that semiclassical gravity hold when the curvature is smaller than planck scale. But the small corrections theorem shows that with this assumption we cannot resolve the information paradox. The fuzzball paradigm has provided a second mode of breakdown of the semiclassical approximation, which happens when a curvature of order 1/L^2 extends over a distance of order L or larger, regardless of how big L is. We will discuss the `vecro' picture of the quantum gravity vacuum that explains this breakdown, and explain how it can impact cosmological evolution at the scale of the cosmological horizon.

Edgar Shaghoulian: The central dogma and entanglement in de Sitter space

The central dogma of black hole physics – which says that from the outside a black hole can be described in terms of a quantum system with Area/4G degrees of freedom evolving unitarily – has recently been supported by computations indicating that the interior of the black hole is encoded in the Hawking radiation of the exterior. In this talk we will discuss whether such a dogma for cosmological horizons has any support from similar computations.The fact that the de Sitter bifurcation surface is a minimax surface (instead of a maximin surface in the case of black holes) causes problems with this interpretation when trying to import calculations analogous to the AdS case. This suggests placing the holographic dual on the de Sitter horizon itself, where we formulate a two-sided extremization prescription for computing entanglement entropy in the holographic dual. We find answers consistent with general expectations for a quantum theory of de Sitter space, including a vanishing total entropy and an entropy of A/4G when restricting to a single static patch. We will also explore some of its more exotic predictions.

Lárus Thorlacius: Holographic black hole evolution

We revisit the black hole information problem in the context of the AdS/CFT correspondence. The formation and evaporation of small AdS black holes is governed by unitary time evolution in the dual gauge theory but how does this translate to the gravitational theory? We argue that the eigenstate thermalisation hypothesis can explain the validity of semiclassical gravity for local bulk observables. Small AdS black holes correspond to states with finite energy width in the holographic dual, and observables that are smooth functions on the classical phase space will self-average over a large number of energy eigenstates, exponential in the Bekenstein-Hawking entropy, giving expectation values that are consistent with semiclassical gravity up to small corrections. On the other hand, the semiclassical bulk description breaks down at leading order for transition amplitudes which probe the unitary evolution of the theory.

Roberto Volpato: A fresh view on string orbifolds

In quantum field theory, an orbifold is a way to produce a new theory from and old one by gauging a finite global symmetry. In quantum gravity theories, there are (conjecturally) no global symmetries, so this definition of orbifold does not apply directly. String theoretical orbifolds can be defined as gauging of global symmetries on the worldsheet CFT describing the dynamics of the fundamental string. While the definition of QFT orbifold depends only on intrinsic properties of the theory, such as its group of global symmetries, the string theoretical orbifold is not “democratic” among all its dynamical objects, so it requires choosing a particular duality frame. We discuss how a duality independent string orbifold procedure might be defined. This analysis sheds some new light on symmetries and orbifolds in string theory, and suggests new directions for generalizations.

Aron Wall: Cauchy slice holography

I will explain how to use the T^2 deformation to reformulate the holographic principle in terms of a dual theory which lives on Cauchy slices, so that time is the emergent dimension. This new formulation interfaces with the usual AdS/CFT duality, and defines a dictionary mapping between boundary CFT states and bulk Wheeler-DeWitt states. Based on arXiv:2204.00591.