Workshop on

Black Holes, BPS and Quantum Information

September 20-24, 2021

Black Holes, BPS and Quantum Information

September 20-24, 2021

- Sergei Alexandrov

University of Montpellier ## D-instantons in Type II string theory on Calabi-Yau threefolds

2021/09/22, 14:00 — 15:00.Euclidean D-branes wrapped on non-trivial cycles of a Calabi-Yau threefold are known to affect the metric on the hypermultiplet moduli space determining the effective action of type II strings on such manifolds. After reviewing the existing results on the instanton corrected metric following from a combination of constraints imposed by supersymmetry and dualities, I'll show how the D-instanton effects can be computed by a direct worldsheet approach. It required solving several conceptual and technical problems and can now be extended to compactifications with lower supersymmetry.

The talk is based on joint work with A. Sen and B. Stefanski.

- Kathrin Bringmann

University of Cologne ## Asymptotic properties of modular type objects

2021/09/23, 09:00 — 10:00.In my talk I will report about various asymptotic results pertaining to modular type objects as well as functions whose modular symmetries are broken.

- Pawel Caputa

University of Warsaw ## Geometry of Krylov Complexity

2021/09/20, 10:15 — 11:15.In this talk I will describe the notion of the operator growth and Krylov complexity. In particular, I will discuss its geometric interpretation and possible applications to holographic CFTs.

This talk will be based on: arXiv:2109.03824 [hep-th].- Stéphane Detournay

Université Libre de Bruxelles ## The 3d black string and its dual

2021/09/23, 15:15 — 16:15.About 30 years ago, Horne and Horowitz described a three-dimensional black string solution sharing many qualitative features of the Reissner-Nordstrom black hole. Viewing the black string as a certain deformation of the BTZ black hole, we will give evidence that its field theory dual consists in an irrelevant deformation of a 2d CFT of the $T \bar{T}$ form.

- Roberto Emparan

ICREA & University of Barcelona ## Digging traversable wormholes

2021/09/21, 14:00 — 15:00.In recent years there have appeared several constructions of traversable wormholes, in four and other dimensions, which only involve physically acceptable, controllable ingredients. They connect in deep ways many aspects of gravity, quantum field theory, and quantum information. I will discuss several features of these constructions, with a focus on traversability, connectivity between multiple mouths, and the (im)possibility of time travel.

- Francesca Ferrari

ICTP Trieste ## 3d Modularity and Supergroup Chern-Simons theory

2021/09/24, 10:15 — 11:15.Quantum modular forms emerged in the 1980's from the study of (WRT) invariants of 3-dimensional manifolds. More recently, new 3-manifold invariants, known as homological blocks, have been discovered. Physically these invariants are given by the half-index of BPS states of a system of fivebranes wrapping a 3-manifold. In this talk, I will describe the central role played by quantum modular forms in the study of 3-manifold invariants. In addition, I will introduce homological blocks for supergroups and provide an explicit algorithm to calculate these q-series for a class of plumbed 3-manifolds.

- Federico Galli

University of Florence ## Aspects of holographic complexity

2021/09/20, 15:15 — 16:15.I will discuss results in the framework of holographic complexity. In the first part, I will describe the variation of holographic complexity for two nearby target states and the resulting "first law of complexity" following from Nielsen's approach. As a concrete example, we will examine perturbations of the vacuum by a scalar field excitation corresponding to a coherent state. In the second part I will consider the influence of rotation on holographic complexity and on circuit complexity in a 2d free scalar TFD state.

- Yang-Hui He

London Institute, Royal Institution & City, University of London & University of Oxford & Nan Kai University ## Machine-Learning Mathematical Structures

2021/09/24, 09:00 — 10:00.We report and summarize some of the recent experiments in machine-learning of various structures from different fields of mathematics, ranging from geometry, to representation theory, to combinatorics, to number theory. We speculate on a hierarchy of inherent difficulty and where string theoretic problems tend to reside.

- Vishnu Jejjala

University of the Witwatersrand ## (K)not machine learning

2021/09/21, 09:00 — 10:00.We present a simple phenomenological formula which approximates the hyperbolic volume of the knot complement based on an evaluation of the Jones polynomial at a complex phase. The error is 2.86% on the first 1.7 million knots. This approximate formula is obtained from reverse engineering a neural network which achieves a similar error after training on 10% of the data. In Chern-Simons language, the phase corresponds to fractional level. We interpret this in terms of the analytic continuation of Chern-Simons theory. After discussing applications of machine learning to other problems in knot theory, we examine machine learning in a broader context and note its applications to holography.

- Abhiram Kidambi

Kavli IPMU ## Generalized Siegel-Weil theorem and Holography

2021/09/22, 09:00 — 10:00.A recent discovery in holography is the idea of not of a particular CFT but rather of an ensemble of CFT's and its gravitational interpretation. In this talk, I will explain my work of the generalization of the recent work of Maloney-Witten and Afkhami-Jeddi et.al. Following a pedagogical introduction to the number theoretic side of the problem, I will talk about the holographic duality that follows from considering the average over toroidal CFTs with gravitational anomalies.

- Robert de Mello Koch

University of the Witwatersrand ## Quantum Error Correction and Holographic Information from Bilocal Holography

2021/09/20, 14:00 — 15:00.Bilocal holography is a constructive approach to the higher spin theory holographically dual to $O(N)$ vector models. Bilocal holography provides a complete bulk/boundary mapping in that it maps the complete set of $O(N)$ invariant degrees of freedom in the CFT, to the complete set of higher spin degrees of freedom. We develop the geometrical properties of this map. After restricting to a suitable code subspace we demonstrate that bilocal holography naturally reproduces the quantum error correcting properties of holography and it gives a robust bulk (entanglement wedge) reconstruction. We argue that finite N relations in the CFT, when interpreted in the dual AdS spacetime, provides relations between degrees of freedom located near the boundary and degrees of freedom deep in the bulk.

- Finn Larsen

University of Michigan ## Black Hole Entropy in AdS: supersymmetry and beyond

2021/09/24, 15:15 — 16:15.Nearly supersymmetric AdS black holes can depart from the strict limit in two distinct ways: a temperature may take them above extremality and a potential may violate a certain constraint. We study these deformations using black hole thermodynamics and CFTs in various dimensions.

- Jan Manschot

Trinity College Dublin ## Scaling Black Holes and Modularity

2021/09/23, 10:15 — 11:15.Scaling solutions are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge carried by a D4-brane in string theory. These partition functions exhibit modular properties as a consequence of S-duality and the AdS$_3$/CFT$_2$ correspondence of the near horizon geometry. For three constituents, we demonstrate that the partition function is a mock modular form of depth two. Upon specialization of the compactification manifold to a K3 fibration, we explicitly evaluate holomorphic parts of these partition functions. Joint work with Aradhita Chattopadhyaya and Swapnamay Mondal.

- Stefano Massai

ETH Zurich ## Stringy black hole microstates

2021/09/24, 14:00 — 15:00.I will discuss new solvable models for the dynamics of strings in asymptotically linear dilaton spacetimes, that offer an exact description of “fuzzball” states in the Hilbert space of two and three-charge black holes. These constructions reveal stringy excitations that become light at the threshold of horizon formation and provide a glimpse of the entropic long string sector in the gravity regime.

- Tatsuma Nishioka

Kyoto University ## Probing Hawking radiation through capacity of entanglement

2021/09/20, 09:00 — 10:00.The capacity of entanglement is one of quantum information measures that plays a similar role as heat capacity in thermodynamics when the replica parameter is regarded as the inverse temperature. We examine whether the capacity of entanglement can probe gravitational phase transitions associated with a black hole evaporation process. In toy models describing Hawking radiation, we find the capacity typically shows a peak or discontinuity around the Page time when the dominant gravitational saddle switches between replica wormholes of different topologies. Similarly the capacity is shown to be sensitive to the dominant gravitational saddle in the JT gravity, being an invaluable diagnostic for a black hole evaporation process.

- Tokiro Numasawa

University of Tokyo ## Wormholes in coupled SYK/NAdS$_2$ and their phase structures

2021/09/21, 15:15 — 16:15.Wormholes are interesting and important configurations in gravity. In particular, recently traversable wormholes and Euclidean wormholes play important roles. To understand these wormholes better, in this talk I will talk about four coupled SYK models and nearly AdS$_2$ gravities. They are generalizations of two coupled SYK models and Nearly AdS$_2$ gravities, which were introduced by Maldacena and Qi. In the SYK model side, we construct a model that couples two copies of two coupled SYK models. In the nearly AdS$_2$ gravity side, we introduce couplings between matter fields in two copies of traversable wormholes.The systems show first order phase transitions at zero temperature by changing couplings, which is understood as the exchange of traversable wormhole configurations in both cases. In nearly AdS$_2$ gravity cases, through the double Wick rotation, traversable wormholes are interpreted as bra-ket wormholes, which gives a connection between bra and ket vectors. After going to the Lorentzian signature, these bra-ket wormholes lead to two closed universes that are entangled with each other as well as matter fields in the flat space without dynamical gravity. We study the effect of projection or entangling operation for matter on flat spaces and they cause phase transitions in bra-ket wormholes, which leads to the pair annihilation of closed universes. Using these bra-ket wormhole configurations, we also discuss the way to embed states in $2d$ holographic CFTs into Hilbert space of many $2d$ free fields.

- Boris Pioline

Sorbonne Université ## From attractor indices to single-centered indices

2021/09/22, 15:15 — 16:15.In quiver quantum mechanics with 4 supercharges, or in four-dimensional string vacua with $N=2$ supersymmetry, the BPS spectrum famously exhibits wall-crossing phenomena. The spectrum is supposed to be simplest in the attractor chamber, where most multi-centered bound states have decayed. However, for quivers with oriented loops there still remain scaling solutions, where the centers can become arbitrarily close to each other. The Coulomb branch formula is a conjectural prescription for subtracting the contributions of scaling solutions and extracting the so called single-centered or pure-Higgs index. I will present some recent progress in deriving this prescription from supersymmetric localization.

Based on arXiv:2103.03205 with Guillaume Beaujard and Swapnamay Mondal.

- Valentin Reys

KU Leuven ## Uncovering the mock nature of single-centered BPS black holes

2021/09/22, 10:15 — 11:15.I will review and expand on some results pertaining to single-centered 1/4-BPS state counting in N=4 string theory compactifications. Their degeneracies are Fourier coefficients of certain mock Jacobi forms arising from the Igusa cusp form. Using an extension of the Hardy-Ramanujan-Rademacher circle method suitable for mock modular forms, and some input from the physics of BPS bound states, an analytic formula for these coefficients has recently been obtained. In parallel, exact methods in supergravity have been used to try and recover such analytic counting directly from the low-energy effective description of the compactifications and the corresponding black hole solutions. I will briefly review these attempts and present some work in progress that aim to bring the supergravity result closer to the exact microscopic answer. Open questions and challenges with this program will be discussed at the end of the talk.

- Martí Rosselló

Instituto Superior Técnico, Universidade de Lisboa ## Rademacher expansion from symplectic symmetries of the Siegel modular form: An $N =4$ counting story

2021/09/23, 14:00 — 15:00.Single centred 1/4 BPS degeneracies in four-dimensional $N=4$ heterotic string theory are generated by $1/\Phi_{10}$. In this talk, we will demonstrate how its $Sp(2, \mathbb{Z})$ symmetries enable us to develop not only a Rademacher expansion for these degeneracies, but also derive the explicit structure underlying the polar states that feed into the expansion. Our results have important implications for using microscopic data to exactly compute gravity path integrals.