Iberian Strings 2021
January 19-22

Online meeting organized at
Instituto Superior Técnico,
Lisboa, Portugal

# Abstracts

Lars Aalsma

## A New Spin On The Weak Gravity Conjecture 2021/01/19, 17:30 — 18:00

The mild form of the Weak Gravity Conjecture (WGC) requires that (quantum) corrections to extremal charged black holes increase their charge-to-mass ratio. Currently, it is unknown what the minimal assumptions are needed to proof this conjecture. To address this issue, I will reformulate the WGC as a necessary and sufficient condition on the stress tensor. Applied to rotating BTZ black holes, this condition suggests a spinning WGC, which I proof for corrections generated by fields holographically dual to relevant deformations. Imposing both the charged and spinning WGC on a five-dimensional black string and compactifications thereof, I derive new positivity bounds on Wilson coefficients. These bounds are stronger than those obtained from the charged WGC alone and further constrain effective theories compatible with quantum gravity. Based on arXiv:2011.05337 with Alex Cole, Gregory Loges and Gary Shiu.

Roberto Vega Álvarez
Instituto Superior Técnico, Universidade de Lisboa

## Resurgent properties of minimal string theory: part I 2021/01/21, 16:00 — 16:30

In these talks we will report the findings of our unpublished work on resurgent properties of the Painlevé I and II equations. These equations play a fundamental role in Minimal String Theories as the specific heat of 2D (Super)-Quantum Gravity. We will do a short introduction to the topic of resurgence and explain the role of Stokes constants when constructing solutions to these equations. While reviewing these tools, we will present our new method for numerically calculating these constants in very general setups to reasonably high precision.

Universitat de Barcelona

## Violations of weak cosmic censorship in black hole collisions 2021/01/22, 11:30 — 12:00

We simulate collisions of stable rotating black holes in six and seven dimensions. We find that if the angular momentum of the system is sufficiently large, the post-merger configuration is an elongated dumbbell which is Gregory-Laflamme unstable. As such, it displays a cascade of satellite formation which ultimately leads to pinching off of the horizon, thus violating the weak cosmic censorship conjecture.

Pedro Aniceto
Instituto Superior Técnico, Universidade de Lisboa

## $R^2$ corrected $AdS_2$ holography 2021/01/19, 15:30 — 16:00

We approach the problem of constructing the holographic dictionary for $AdS_2/CFT_1$ in the context of higher derivative gravitational actions in $AdS_2$. We focus on $S_2$ reductions of four-dimensional $N=2$ Wilsonian effective actions with Weyl squared interactions restricted to constant scalar backgrounds. BPS black hole near-horizon spacetimes fall into this class of backgrounds and, by identifying the boundary operators dual to the bulk fields, we explicitly show how the Wald entropy of the BPS black hole is holographically encoded in the anomalous transformation of the operator dual to a composite bulk field. Additionally, using a 2d/3d lift, we show that the $CFT$ holographically dual to $AdS_2$ is naturally embedded in the chiral half of the $CFT_2$ dual to the $AdS_3$ spacetime, and we identify the specific $CFT_1$ operator that encodes the chiral central charge of the $CFT_2$.

Matteo Baggioli
Jiao Tong University Shanghai

## How small hydrodynamics can go 2021/01/19, 11:00 — 11:30

Numerous experimental and theoretical results in liquids and plasmas suggest the presence of a critical momentum at which the shear diffusion mode collides with a non-hydrodynamic relaxation mode, giving rise to propagating shear waves. This phenomenon, labelled as $k$-gap, could explain the surprising identification of a low frequency elastic behavior in confined liquids. More recently, a formal study of the perturbative hydrodynamic expansion showed that critical points in complex space, such as the aforementioned $k$-gap, determine the radius of convergence of linear hydrodynamics, its regime of applicability. In this talk, we combine the two new concepts and we study the radius of convergence of linear hydrodynamics in real liquids by using several data from simulations and experiments. We generically show that the radius of convergence increases with temperature and it surprisingly decreases with the interactions coupling. More importantly, we find that such radius is universally set by the characteristic interatomic distance of the liquid, which provides a natural microscopic bound. We finally compare our results with those from holographic theories.

Salvatore Baldino
Instituto Superior Técnico, Universidade de Lisboa

## Seiberg-Witten theory, string theory and WKB analysis 2021/01/21, 11:00 — 11:30

In this talk, we will explore the relationship between non critical string theories, $SU(2)$ supersymmetric gauge theories and WKB analysis. In particular, we will examine the role of Seiberg-Witten geometry in the context of $SU(2)$ theories, and how this is related to the concept of string duality. We will examine the role of WKB analysis in solving the equations that come out in this context. We will focus on the physical interpretation of the various quantities that can be computed in WKB analysis, and how they can be related to observables in Seiberg-Witten theory or string theory. We will conclude by presenting the author's work on WKB analysis of finite difference equations, that naturally appear in this context.

Yago Bea
Queen Mary London

## New Insights from Real-time Dynamics 2021/01/19, 12:30 — 13:00

We use together relativistic hydrodynamics, numerical relativity and holography to address novel problems. We go beyond the state of the art in several directions. First, we construct a gravitational solution of a fully localized, compact black hole falling through the Poincare horizon in an asymptotically $AdS$ setting. By holography, this solution is mapped to a localized plasma surrounded by vacuum that disperses away. Second, we study the applicability of hydrodynamics, and in particular we perform time evolution using causal theories of hydrodynamics, for the first time in the context of holography. Third, we also go beyond the state of the art by performing time evolution of the recent generalized frame formulation of hydrodynamics (BDNK), for the first time. Fourth, our setting constitutes a new arena to the fluid/gravity duality, being outside the usual assumptions. Our results may provide relevant insights into the quark-gluon plasma physics and astrophysical scenarios.

Nana Geraldine Cabo Bizet

## Testing Swampland Conjectures with Machine Learning 2021/01/22, 15:30 — 16:00

We consider Type IIB string theory compactification on an isotropic torus with geometric and non geometric fluxes. Employing supervised machine learning, consisting of an artificial neural network coupled to a genetic algorithm, we determine more than sixty thousand flux configurations yielding a scalar potential with at least one critical point. Stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the Refined de Sitter Conjecture. Hierarchical fluxes favor perturbative solutions with small values of the vacuum energy and moduli masses, as well as scenarios with the lightest modulus mass much smaller than the AdS vacuum scale.

Dmitri Bykov
MPI Physik Munich

## Sigma models as Gross-Neveu models 2021/01/20, 16:30 — 17:00

I will show that there is a wide class of integrable sigma models, which includes $CP^{n-1}$, Grassmannian, flag manifold models, that are equivalent to bosonic (and mixed bosonic/fermionic) chiral Gross-Neveu models. The established equivalence allows to effortlessly construct trigonometric/elliptic deformations, provides a new look on the supersymmetric theory and on the cancellation of anomalies in the integrability charges. Using this formalism, we develop criteria for constructing quantum integrable models related to quiver varieties. Based on arXiv:2006.14124 and arXiv:2009.04608

Pablo Cano
KU Leuven

## Novel higher-curvature variations of $R^2$ inflation 2021/01/19, 11:30 — 12:00

Higher-curvature corrections to the gravitational action are a definite prediction of string theory and they may play an important role in the early universe. Indeed, one of the most successful inflationary scenarios is based on the Lagrangian $R+R^2$, but the effect of more general corrections is not yet fully understood. In this talk I will describe extensions of the $R+R^2$ model with a recently identified type of curvature corrections that keep the cosmological equations second-order and which therefore give rise to a well-behaved cosmological evolution. We use holographic methods to constrain the couplings of the new operators and then we derive the predictions for the power spectrum of tensor and scalar primordial fluctuations. The predicted values of the scalar spectral index and the tensor-to-scalar ratio turn out to lie within experimental constraints, but observations in the near future may be able to distinguish the presence of higher-curvature corrections.

Mattia Cesaro

## Kaluza-Klein fermion mass matrices from Exceptional Field Theory and $N=1$ spectra 2021/01/21, 12:00 — 12:30

Using Exceptional Field Theory, the infinite-dimensional mass matrices for the gravitino and spin-1/2 Kaluza-Klein perturbations above a class of anti-de Sitter solutions of M-theory and massive type IIA string theory with topologically-spherical internal spaces can be determined. These mass matrices can be employed to compute the spectrum of Kaluza-Klein fermions about some solutions in this class with internal symmetry groups containing $SU(3)$. Combining these results with previously known bosonic sectors of the spectra, I will present the complete spectra about some $N=1$ and some non-supersymmetric solutions in this class, together with certain generic features they are shown to enjoy.

Mihailo Cubrovic

## Lyapunov spectra in traversable wormholes and their holographic duals 2021/01/20, 11:00 — 11:30

We study the decay of out-of-time-ordered correlators (OTOC) in an AdS traversable wormhole and its gravity dual, two coupled Sachdev-Ye-Kitaev models ("left" and "right" subsystem). The gravity calculation of OTOC involves perturbative equations more involved than for a black hole, as the perturbation has complex kinematics and can bounce back and forth through the wormhole many times. The outcome is a phase diagram with three regions. One is black-hole like with uniform exponential growth and the Lyapunov exponent $\lambda=2\pi T$ ("the chaos bound"). The intermediate phase has OTOCs with a spectrum of different exponents for different operator modes, all below the maximal chaos bound. The third phase has exponentially small Lyapunov exponents, behaving as $\exp(-1/T)$, in accordance with a recent field-theory calculation in the literature. The Lyapunov spectrum carries more information than just the maximum exponent: it can be related e.g. to teleportation fidelity from left to right subsystem.

Frank Eisenhauer
Max Planck Institute for extraterrestrial Physics

## The Discovery of the Massive Black Hole in the Center of the Galaxy. Outreach colloquium on the occasion of The Nobel Prize in Physics 2020 2021/01/20, 17:30 — 18:30

Outreach colloquium on the discovery of a supermassive compact object at the centre of our galaxy.

Black Holes are among the most mysterious objects in the Universe. They are so massive and compact that nothing - not even light - can escape their gravity. The 2020 Nobel Prize in Physics was awarded to Roger Penrose for showing that these exotic objects are a direct consequence of Einstein's general theory of relativity, and to Reinhard Genzel and Andrea Ghez for the discovery of such a monster in the center of our Galaxy. Our presentation will portrait the 40 year journey from the first indications to the overwhelming observational evidence for a extremely heavy and compact object in the Galactic Center, for which a supermassive black hole is the only known explanation. Using the world's largest telescopes and most advanced optics technology, astronomers can now follow the stars orbiting the central object, precisely measure its mass, and detect the stunning effects of general relativity. In our talk we will present both the spectacular observations and the technology behind.

Zachary Elgood

## The first law of heterotic stringy black hole mechanics at zeroth order in $\alpha'$ 2021/01/22, 16:30 — 17:00

We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in $\alpha'$, using Wald's formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In the presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.

Roberto Emparan
ICREA Barcelona

## The ultimate trap: a tale of horizons, singularities, and black holes. Outreach colloquium on the occasion of The Nobel Prize in Physics 2020 2021/01/21, 17:30 — 18:30

Outreach colloquium on black hole formation as a robust prediction of the general theory of relativity.

More than fifty years ago, a young mathematician called Roger Penrose revolutionized the study of gravity and spacetime by introducing the idea of a “trapped surface”: a region where the pull of gravity is so strong that spacetime is inevitably led to a mysterious singularity. This result is so important that last year Penrose was awarded the Nobel Prize in Physics for “showing that Einstein's theory leads to the formation of black holes, those monsters in time and space”. Isn't it fascinating? Sure, but, actually, what does it mean?

Roberto Emparan
ICREA Barcelona

## Quantum BTZ black hole 2021/01/22, 10:00 — 10:30

The study of quantum effects on black holes including their gravitational backreaction is an important but notoriously hard problem. I will begin by reviewing how the framework of braneworld holography allows to solve it for strongly-coupled quantum conformal fields. Then I will describe a holographic construction of quantum rotating BTZ black holes (quBTZ) using an exact dual four-dimensional bulk solution. Besides yielding the quantum-corrected geometry and the renormalized stress tensor of quBTZ, we use it to show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, rather non-trivially satisfies the first law of thermodynamics, while the Bekenstein-Hawking-Wald entropy does not.

Johanna Erdmenger
University of Würzburg

## Information geometry and QFT 2021/01/20, 09:00 — 10:00

Review lecture on Information geometry and quantum field theory.

The AdS/CFT correspondence is the most prominent example of a duality relating a quantum theory of fields (without gravity) to a gravity theory. As proposed by Maldacena in 1997, the AdS/CFT conjecture is strongly motivated by the duality of D-branes in the open and the closed string theory pictures in the the near-horizon limit. Since then, the question has arisen if a duality relating quantum field theory to gravity may be established more generally, leading to further insights into the structure of quantum gravity. This development is fuelled in particular through new developments involving concepts from quantum information, following the holographic entanglement entropy proposal of Ryu and Takayanagi in 2006. In this talk, I will review very recent progress in this area, considering insights from information geometry, a branch of mathematics, in particular. Moreover, I will consider bulk reconstruction, modular flows, and computational complexity. Insights from black hole physics and information theory have led to new developments in quantum field theory. As examples, I will present implications of the Fisher metric curvature for phase transitions, complexity proposals for conformal field theories and non-local modular flows.

Mikel Sanchez Garitaonandia
University of Barcelona

## Bubble Mergers from Holography 2021/01/19, 12:00 — 12:30

Phase separated states are a key feature of theories with a first order thermal phase transition at infinite volume. Such states can dynamically appear as end states in the real time evolution of the spinodal-instability. Holography stands as an appealing tool in order to simulate out-of-equilibrium, non-linear processes which yield the final phase separated state. In this talk, we will focus on one such process - the dynamics of bubble mergers. We will study the details of the mergers for a range of speeds, including relativistic ones, and we will discuss three different important scenarios.

Jerome Gauntlett
Imperial College London

## Geometric Extremization for AdS/CFT and Black Hole Entropy 2021/01/21, 09:00 — 10:00

Review lecture on Geometric Extremization for AdS/CFT and Black Hole Entropy.

Certain physical properties of SCFTs with an abelian R-symmetry are determined by the R-symmetry. Furthermore, the R-symmetry can be obtained by an extremization principle. If the SCFT has a holographic dual there is a geometric version of the extremization principle which is a powerful tool in identifying and studying the dual SCFT as well as being of intrinsic geometric interest.

We focus on supersymmetric $AdS_3 \times Y^7$ solutions of type IIB supergravity dual to $N=(0,2)$ SCFTs in $d=2$, as well as $AdS_2 \times Y^9$ solutions of $D=11$ supergravity dual to $N=2$ supersymmetric QMs, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. Our results allow us to identify infinite classes of $d=2$ SCFTs and susy QMs that are obtained by by wrapping higher dimensional SCFTs on Riemann surfaces. For the latter case our results provide a microstate counting of the entropy of a class of supersymmetric black holes in $AdS_4$.

Diego Gutiez
University of Oviedo

## Deep learning generation of holographic geometries from $q \bar q$ potential data 2021/01/20, 15:30 — 16:00

The AdS-CFT correspondence is a very powerful tool that allows us to compute field theory observables from a gravity dual. One of the hurdles of this duality is to obtain a dual geometry from certain QFTs such as QCD. In the past few years, some efforts have been made to use deep learning techniques to generate the dual geometry from some known data in the QFT. In particular, Hashimoto et al. were able to propose some geometries dual to QCD using this kind of techniques. The aim of our work is to reproduce the metric of a black hole from the $q \bar q$ potential in a deconfined phase. In particular, we compare the potential generated by a given geometry and compare it to the QFT results in order to train the net.

Yang-Hui He
City, University of London & University of Oxford

## Machine learning in field theory and string theory 2021/01/20, 14:30 — 15:30

Review lecture on Machine learning in field theory and string theory.

Mario Herrero
SISSA

## Amplitudes Positivity and IR-UV connections in Graviton Exchange 2021/01/21, 12:30 — 13:00

Positivity bounds are standard tools to assess the validity of EFTs for which a unitary, local and Lorentz Invariance UV completion is assumed. They impose positivity of certain (combination of) Wilson coefficients by connecting IR physics to features of the UV completion through dispersion relations of scattering amplitudes. If the corresponding EFT does not satisfy these bounds, it is assumed to lay on the Swampland.

However, the standard derivation of positivity bounds fails when the exchange of a massless particle is possible, which excludes the very important case of gravitational interactions. In this talk we show how to derive new positivity bounds that take into account this issue. We generalize the standard derivation by writing dispersion relations which are valid when production of massless particles is included.

Furthermore, we show that one can obtain efficient bounds in the case of gravity if one assumes the high energy limit of the scattering amplitude to be of the Regge form, as implied from String Theory. We will discuss implications of these bounds for different physical settings, such as models of interacting scalar fields, scalar QED, and the Weak Gravity Conjecture.

Johannes Lahnsteiner
University of Groningen

## A Non-Relativistic Limit of NS-NS Gravity 2021/01/20, 12:00 — 12:30

In this talk, I describe recent progress in understanding the background field dynamics of the non-relativistic string theory pioneered by Gomis and Ooguri. It is well-known that the underlying string sigma model can be obtained via a limiting procedure — based on a crucial cancellation of infinities — from the relativistic Polyakov model. I show that a similar, subtle limit of the effective supergravity description can be defined — giving rise to a non-relativistic analog of NS-NS gravity. The results are compared with constraints on the background geometry coming from (one-loop) beta function calculations. In the final part of my talk, I will comment on non-relativistic T-duality, p-brane solutions, and potential applications to non-relativistic holography.

Gabriel Larios

## Kaluza-Klein spectra and consistent truncations 2021/01/21, 11:30 — 12:00

Kaluza-Klein spectra on string/M-theory solutions depend significantly on whether the solution can be obtained from uplift of a maximal gauged supergravity. For some solutions of M-theory, mIIA and IIB obtained from uplift, I will present the spectrum of KK gravitons and discuss a persistent form of universality when solutions with same (super)symmetry and supergravity spectrum are present in different theories. In the second part of the talk, I will discuss the spectrum of KK gravitons around the $N=2 \ AdS_4$ solution that is dual to the IR of a cubic deformation of ABJM. This solution cannot be obtained from uplift of an $N=8 \ D=4$ theory, and this seems to be linked to the fact that its metric cannot be isometrically embedded in $R^8$. Further, the allocation of modes with different spins in $N=2$ supermultiplets cannot be made KK level by KK level, but needs space invaders.

Alejandro Vilar Lopez
University of Santiago de Compostela

## Holographic entanglement entropy for perturbative higher-curvature gravities 2021/01/19, 16:30 — 17:00

The very well-known prescription of Ryu and Takayanagi for computing holographic entanglement entropy (HEE) in Einstein gravity was extended to higher-curvature theories in works by Xi Dong and Joan Camps. Unfortunately, obtaining the entanglement entropy functional involved an obscure procedure in which the Riemann tensors had to be split and weighted according to a certain prescription. In this talk, I will show that there is a much simpler way to understand this procedure, at least when corrections to Einstein gravity are perturbative. By means of this new way to obtain the HEE functional, I will also show some explicit results for cubic theories, employing them to obtain universal terms of the entanglement entropy for various symmetric regions in the boundary field theory. In particular, the universal function characteristic of corner regions in $d=3$ can be shown to be modified by cubic corrections. This is the first example of a holographically obtained corner function different to the Einstein gravity one.

David Mateos
University of Barcelona

## Strong-coupling dynamics and entanglement in de Sitter space 2021/01/19, 10:00 — 10:30

We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate $H$. The gauge theory is non-conformal with a characteristic mass scale $M$. We solve Einstein’s equations numerically and determine the time evolution of homogeneous gauge theory states. If their initial energy density is high compared with $H^4$ then the early-time evolution is well described by viscous hydrodynamics with a non-zero bulk viscosity. At late times the dynamics is always far from equilibrium. The asymptotic late-time state preserves the full de Sitter symmetry group and its dual geometry is a domain-wall in $AdS_5$. The approach to this state is characterised by an emergent relation of the form $P = w E$ that is different from the equilibrium equation of state in flat space. The constant $w$ does not depend on the initial conditions but only on $H/M$ and is negative if the ratio $H/M$ is close to unity. The event and the apparent horizons of the late-time solution do not coincide with one another, reflecting its non-equilibrium nature. In between them lies an “entanglement horizon” that cannot be penetrated by extremal surfaces anchored at the boundary, which we use to compute the entanglement entropy of boundary regions. If the entangling region equals the observable universe then the extremal surface coincides with a bulk cosmological horizon that just touches the event horizon, while for larger regions the extremal surface probes behind the event horizon.

Thomas Mertens
Ghent University

## JT gravity 2021/01/19, 14:30 — 15:30

Review lecture on JT gravity.

In this review talk, I will give an overview of several of the main developments in lower dimensional gravity (and in particular Jackiw-Teitelboim (JT) gravity) that have happened in the last couple of years. In particular, emphasis will be placed on the structure and solution of the model in terms of the Schwarzian wiggly curve and Riemann surface technology. At the semi-classical level, this model provides a concrete set-up for understanding some of the recent developments in the information paradox. At the quantum gravity level, higher topological corrections to amplitudes lead to features of discreteness of the underlying system and make contact with Maldacena's version of the information paradox. In particular, JT gravity itself can be written entirely as a matrix integral. We end with some discussions on how generic these lessons are, in particular for other models of quantum gravity.

Alessandro Mininno

## Dynamical Tadpoles and Weak Gravity Constraints 2021/01/22, 17:30 — 18:00

Non-supersymmetric string models are plagued with tadpoles for dynamical fields, which signal uncanceled forces sourced by the vacuum. We argue that in certain cases, uncanceled dynamical tadpoles can lead to inconsistencies with quantum gravity, via violation of swampland constraints. We describe an explicit realization in a supersymmetric toroidal $Z_2 \times Z_2$ orientifold with $D7$-branes, where the dynamical tadpole generated by displacement of the $D7$-branes off its minimum leads to violation of the axion Weak Gravity Conjecture. In these examples, cancellation of dynamical tadpoles provides consistency conditions for the configuration, of dynamical nature (as opposed to the topological conditions of topological tadpoles, such as RR tadpole cancellation in compact spaces). We show that this approach provides a re-derivation of the Z-minimization criterion for $AdS$ vacua giving the gravitational dual of a-maximization in $4d \ N=1$ toric quiver SCFTs.

Ángel Jesus Murcia

## Electromagnetic Quasitopological Gravities 2021/01/19, 17:00 — 17:30

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function $f(r)=-g_{tt}=1/g_{rr}$. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for $f(r)$. Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.

Edvard Musaev
Moscow Institute of Physics and Technology

## Non-abelian U-duality of M-theory background 2021/01/20, 12:30 — 13:00

Backgrounds of perturbative string theory are known to enjoy various duality symmetries, relating different points in the space of vacua. Among these are the perturbative T-duality symmetries, relating backgrounds with a certain amount of space-time isometries to dual field configurations. Depending on the algebra of Noether currents one finds abelian, non-abelian or Poisson-Lie T-duality symmetries. Non-abelian U-duality symmetry is a generalisation of Poisson-Lie T-duality transformation to the case of 11-dimensional backgrounds, where the string becomes non-perturbative. This is based on the concept of exceptional Drinfeld double, which is a generalisation of the classical Drinfeld double Lie algebra to Leibniz algebras. In this talk this algebraic construction is reviewed, a generalisation of Buscher rules to the case of non-abelian U-duality of group manifold backgrounds is described and a set of examples is presented. The related concept of tri-vector and six-vector deformations is also discussed and the corresponding generalisation of the classical Yang-Baxter equation governing integrable bi-vector deformations is overviewed.

Kevin Nguyen
King's College London

## Slow scrambling in extremal BTZ and microstate geometries 2021/01/20, 11:30 — 12:00

Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries.

I will first discuss OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display "slow scrambling", characterized by cubic (rather than exponential) growth. Then I will discuss the extent to which these OTOCs are modified in certain "superstrata", horizonless microstate geometries corresponding to these black holes. Rather than an infinite throat ending on a horizon, these geometries have a very deep but finite throat ending in a cap. We find that the superstrata display the same slow scrambling as maximally rotating BTZ black holes, except that for large enough time intervals the growth of the OTOC is cut off by effects related to the cap region.

Malcom Perry
DAMTP, Cambridge

## Soft Charges, Soft Hair and Black Hole Entropy 2021/01/19, 09:00 — 10:00

Review lecture on Asymptotic symmetries in gravity.

I will describe the concept of soft charge emerging from the nature of the BMS group. An explicit construction of the supertranslation charges and their integrability will be presented together with arguments as to why this leads to conserved charges. I will extend this to other asymptotic charges. I will then explain how to construct soft black hole hair and show how it can be used to determine the Hawking black hole entropy through holography. I will conclude by looking at the implications for the information paradox.

Anayeli Ramirez
University of Oviedo

## $1/4$ BPS $AdS_3/CFT_2$ 2021/01/21, 10:00 — 10:30

With a focus in their CFT interpretation, in this talk we study $AdS_3$ solutions in massive type IIA supergravity and $AdS_2$ solutions in type IIB supergravity. From the geometry, we engineer the dual CFT with well known tools and propose a duality with a precise family of quivers. Additionally, we compute field theory and holographic central charges showing a clean matching in both descriptions.

Martí Rosselló
Instituto Superior Técnico, Universidade de Lisboa

## Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N} =4$ CHL models 2021/01/22, 12:00 — 12:30

We use continued fractions to perform a systematic and explicit characterization of the decays of two-centred dyonic black holes in $4D$ $\mathcal{N} =4$ heterotic $\mathbb{Z}_N$ CHL models. Thereby we give a new exact solution for the problem of counting decadent dyons in these models.

Daniel Hernández Ruipérez
University of Salamanca

## Supermoduli of supersymmetric curves with punctures 2021/01/21, 14:30 — 15:30

Review lecture:

We introduce super schemes (super algebraic varieties) and super analytic spaces and their basic properties. We then focus on SUSY curves (supersymmetric Riemann surfaces) without and with NS and RR punctures and construct a supermoduli for them. It has the structure of an Artin algebraic superspace, that is, it is the quotient of an étale equivalence relation of superschemes (superalgebriac varieties). We also report on compactifications of the supermoduli.

Leonardo Santilli

## $T \bar{T}$–deformation of $q$-Yang-Mills theory 2021/01/20, 16:00 — 16:30

I will present the $T \bar{T}$-perturbed version of $q$-deformed two-dimensional Yang-Mills theory. I will show that the operator $T \bar{T}$ spoils the factorization of the partition function into chiral/anti-chiral sectors. On the other hand, it preserves a large $N$ third order phase transition, although modifying the phase diagram. Implications for the entanglement entropy at large $N$ will be discussed as well. I will conclude with comments on the potential applications of these results to the Bethe/gauge correspondence and to four-dimensional supersymmetric theories.

Based on joint work with Richard J. Szabo and Miguel Tierz, arXiv:2009.00657

Martin Sasieta

## A Momentum/Complexity Correspondence 2021/01/20, 10:00 — 10:30

Holographic Volume Complexity naturally incorporates the notion of a Momentum/Complexity correspondence. This correspondence formalizes the idea that gravitational clumping of matter increases the complexity of the quantum state. For purely gravitational states, there is no clear momentum candidate aside from perturbative definitions. A generalization of the Momentum/Complexity correspondence is needed to interpret the gravitational contribution as arising from the Weyl tensor of spacetime.

Max Schwick
Instituto Superior Técnico

## Resurgent properties of minimal string theory: part II 2021/01/21, 16:30 — 17:00

We will illustrate the importance of the above concepts in known solutions of the Painlevé equations (tronquée and tritronquée phases). Furthermore, we will expand on the above solutions by introducing some specific characteristics of these equations like resonance, relations between Stokes constants.Then, we will expand on this by explaining a conjecture on the analytic form of these constants that has been checked with our numerical method up to very high precision. Finally, we will talk about possible future directions.

Lárus Thorlacius
University of Iceland

## Entanglement islands 2021/01/22, 09:00 — 10:00

Review on Entanglement islands.

Marija Tomasevic
Universitat de Barcelona

## Multi-mouth traversable wormholes 2021/01/22, 11:00 — 11:30

We describe the construction of traversable wormholes with multiple mouths in four spacetime dimensions and discuss associated quantum entanglement. Our solutions are asymptotically flat up to the presence of magnetic fluxes that extend to infinity. The construction begins with a two-mouth traversable wormhole supported by backreaction from quantum fields. Inserting a sufficiently small black hole into its throat preserves traversability between the original two mouths. This black hole can be the mouth of another wormhole connecting the original throat to a new distant region of spacetime. Our wormholes are traversable between any pairs of mouths. This work is based on arxiv:2012.07821.

Pablo Enmanuel León Torres
University of Antofagasta

## Massive supermembrane in ten non-compact dimensions 2021/01/22, 12:30 — 13:00

We discuss a formulation of the M2-brane theory in ten non-compact dimensions that exhibits mass terms in the Hamiltonian. The existence of these mass terms improves the quantum behaviour of the theory in comparison with the known compactifications of the M2 to ten dimensions. On the other hand, this formulation of the M2-brane can be interpreted as a realization in ten non-compact dimensions of the central charge condition. This result could be interesting, since it represent another well behaved sector of the M2-brane and it might yield new information about massive Romans supergravity in ten dimensions.

Timo Weigand
University of Hamburg

## The Swampland - From Conjectures to Theorems 2021/01/22, 14:30 — 15:30

Review lecture on The Swampland.

The swampland’ has become known as a term to describe effective field theories which, while consistent as quantum field theories, cannot be completed into fully consistent theories of quantum gravity. A growing web of conjectures has been developed in the literature as to when a theory belongs to the swampland. In this talk I will review some of these so-called Quantum Conjectures’, summarise the general and often times heuristic arguments in their support and highlight various connections between them. Despite the speculative character of many of the involved ideas, we will see that some of the quantum gravity conjectures can be made extremely precise and even be proven within large classes of string constructions.

Max Wiesner
## Quantum Corrections in 4d $N=1$ Infinite Distance Limits and the Weak Gravity Conjecture 2021/01/22, 17:00 — 17:30
We study quantum corrections in four-dimensional theories with $N = 1$ supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of $N = 1$ supersymmetric F-theory compactifications to four dimensions including perturbative $\alpha'$ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corrections obstruct precisely those limits in which the scale of the emergent critical string would lie parametrically below the Kaluza-Klein scale. Limits in which the tension of the asymptotically tensionless string sits at the Kaluza-Klein scale, by contrast, are not obstructed.
In the second part of the talk we discuss the effect of quantum corrections for the Weak Gravity Conjecture away from the strict weak coupling limit. We propose that gauge threshold corrections and mass renormalisation effects modify the super-extremality bound in four dimensions. For the infinite distance limits in F-theory the classical super-extremality bound is generically satisfied by a sublattice of states in the tower of excitations of an emergent heterotic string. By matching the F-theory $\alpha'$-corrections to gauge threshold corrections of the dual heterotic theory we predict how the masses of this tower must be renormalised in order for the Weak Gravity Conjecture to hold at the quantum level.
## $5$d SCFTs, 5-brane webs and (orthosymplectic) magnetic quivers 2021/01/21, 15:30 — 16:00
The Higgs branches of $5d \ N=1$ SQCD theories at infinite gauge coupling (UV superconformal fix point) is often inaccessible via standard tools. The recently introduced concept of magnetic quivers proves to be a powerful tool able to probe the finite and infinite coupling limits in a uniform manner. In this talk, I will focus on $5d \ N=1$ SQCD theories whose Higgs branches at infinite coupling exhibit exceptional global symmetries. By realizing these theories as 5-brane web configurations with orientifold planes, I will discuss how to derive the corresponding orthosymplectic magnetic quivers. This allows us to study the geometry of the enlarged Higgs branches of $5d \ N=1$ theories with $Sp(k)$ and $SO(k)$ gauge groups at the UV fix point.