# Joint Belgian hep-th seminars: academic year 2023-2024

###### 29 May 2024, Brussels

**Eleanor Harris **(ICTP Trieste) |** Edge modes on the horizon** The existence of edge modes living at the entangling surface in certain gauge theories gives rise to entanglement entropy between disconnected regions. Inspired by these results, we can ask what this implies for gravity, which is also a gauge theory. These edge modes have been well studied in the context of Chern-Simons theory, which happily is semi-classically equivalent to three-dimensional gravity. In this setup, we will explore contributions to the entropy of the de Sitter horizon, and explore the possible entanglement nature of this entropy.

**Fabio Ori **(Ghent) |** Geometric interpretation of holographic timelike entanglement entropy**

A new object was recently proposed within the holographic quantum gravity paradigm to probe the emergence of time-like directions in gravitational theories. This timelike entanglement entropy has been computed either by analytic continuation of (spacelike) holographic entanglement entropy to timelike separated subregions, without a direct geometric interpretation, or in three bulk dimensions by merging segments of spacelike and timelike geodesics. We suggest a more general prescription: timelike entanglement entropy emerges as an extremal surface in a holographic geometry whose coordinates become complex variables. This reproduces known results and provides a novel bulk interpretation of timelike entanglement entropy where no obvious piecewise surfaces exist. Relevant applications include the possibility of exploring holographic correlation functions of timelike separated operators as new probes of thermalization of quantum field theories, as well as correlators of quantum fields dual to time-dependent spacetimes, where no real geodesic exists, such as de Sitter universe.

###### 22 May 2024, Leuven

**Mark Mezei **(Oxford) |** On the quantum mechanics of old black holes** The Euclidean gravitational path integral involves a sum over topologies. In this talk, we discuss how topology change can be incorporated into the (Lorentzian) Hilbert space description of quantum gravity. Our proposal leaves the semiclassical space of states intact, but modifies the inner product between them giving rise to a plethora of null states. To illustrate the use of this formalism, we construct the black hole interior volume operator in two-dimensional Jackiw-Teitelboim gravity, compute its expectation value at late times, and discuss its relation to holographic complexity.

**Flavio Tonioni **(KUL) |** Analytic bounds on asymptotic cosmologies**

Any scalar FLRW-cosmology with multi-exponential potentials exhibits a universal bound on late-time cosmic acceleration. We discuss the conditions under which scaling solutions are inevitable late-time attractors for this class of theories. Without the need to find explicit solutions to the cosmological equations, we are also able to identify bounds on the late-time expansion rate of the universe in the presence of additional fields with exponential kinetic couplings to the scalars. We can further see how the contraction rate of cosmologies with negative potentials can be bounded through similar methods. These results endow us with strong analytic tools to discuss cosmological backgrounds that appear, for instance, in some asymptotic corners of string compactifications.

###### 8 May 2024, Brussels

**Gabriel Larios **(Texas A&M) |** AdS3/CFT2 and its marginal deformations** I will present new families of AdS3 solutions in type IIB supergravity that depend continuously on moduli. These holographic conformal manifolds can be captured in consistent truncations down to three-dimensional maximal gauged supergravities, and include Lunin-Maldacena TsT deformations. At different loci in the parameter space, different amounts of (super-)symmetry are preserved, and I will argue that for certain ranges of parameters, even non-supersymmetric vacua might be stable.

**Prahar Mitra **(Amsterdam) |** Phase Space Renormalization and Finite BMS Charges in Six Dimensions**

In this talk, we systematically study the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions, namely those that are analytic near null infinity, admit a non-trivial action of the generalized Bondi-Metzner-van der Burg-Sachs (GBMSW) group, which consists of supertranslations and diffeomorphisms on the celestial sphere. Using the covariant phase space formalism and a new technique that we developed in this paper (phase space renormalization), we renormalize the symplectic potential using local and covariant counterterms. We construct charges that faithfully represent the GBMS algebra. Finally, we show that the semi-classical Ward identities for supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems, respectively.

###### 24 April 2024, Mons

**Sylvain Lavau **(Ruđer Bošković Institute) | **A graded geometric perspective on tensor hierarchies** Tensor hierarchies, as they emerge in gauged supergravity, are differential graded Lie algebras with specific properties. This implies that the space of differential forms taking values in a tensor hierarchy algebra (THA) is also a differential graded Lie algebra L, of which the embedding tensor is a Maurer-Cartan element. Whenever one makes a gauge transformation of the latter, one obtains a homological derivation on the space of forms valued in the THA. In the graded geometric language, this makes L a differential graded Lie algebroid. All relevant physical objects — the gauge fields, the field strengths, the gauge transformations and their commutator — then inherit a very simple graded geometric interpretation. This opens the possibility of unifying many gauge theories (Yang-Mills, Leibniz,…) under one unique formalism. Moreover, the L_infinity algebras associated to such theories are readily obtained from the differential graded Lie algebra by a very simple procedure. The talk will be an overview of some mathematical properties of tensor hierarchy algebras, and of their graded geometric interpretation.

**Tim Adamo **(Edinburgh University) |** Scattering on self-dual black holes**

Tree-level graviton scattering amplitudes provide an on-shell model for wave-wave scattering in general relativity, but computing them with traditional perturbative methods is hard due to the non-polynomial nature of the Einstein-Hilbert action. Over the years, many alternative approaches, which have nothing to do with standard Feynman rules, have enabled the computation of all-multiplicity formulae for graviton scattering in Minkowski spacetime. However, studying graviton scattering in non-perturbative curved spacetimes, like black holes, remains an extremely difficult problem. In this talk, I will discuss a simplification of this problem: graviton scattering on a self-dual black hole (in particular, a self-dual Taub-NUT space). This lets us bring powerful integrability methods to bear while still exhibiting the non-linear and non-perturbative hallmarks of ‘real world’ graviton scattering on black holes.

**Victor Godet **(SISSA Trieste) |** Quantum cosmology as automorphic dynamics**

I will discuss some recent progress on the Wheeler-DeWitt equation with positive cosmological constant. This suggests an equivalence between quantum cosmology in three dimensions and a driven particle on moduli space.

###### 17 April 2024, Brussels

**Markus Dierigl **(Munich) | **Global Symmetries, Dualities, and Bordisms** In this talk I will summarize how duality symmetries of supergravity models can potentially lead to global symmetries. These are associated to deformation classes of spaces with non-trivial duality bundle and classified by so-called bordism groups. Since global symmetries are not allowed for consistent theories of quantum gravity, there need to exist certain objects that break these global symmetries. We will discuss S-duality for type IIB supergravity as well as U-duality for maximal 8d supergravities and explore the necessary symmetry-breaking objects in the various setups, which will lead us to (re)discover many interesting configurations in string theory.

**Ivo Sachs **(Munich) |** Quantum Field Theory in anti- and deSitter Space**

Quantum field theory in anti-deSitter space computes a generating function for conformal field theory correlators. In deSitter it computes the wave function for cosmological correlation functions. The inclusion of loop corrections poses new technical as well as conceptual problems but also reveals interesting insights including a pathology of the O(N) model noticed many years ago by Coleman and Jackiw.

###### 27 March 2024, Ghent

**Mikhail Isachenkov **(University of Amsterdam) | **Double-scaled SYK and q-homogeneous spaces** In this talk I will discuss an application of q-homogeneous spaces to the quest of understanding quantum gravity. Sachdev-Ye-Kitaev (SYK) model, and its double-scaled version (DSSYK), got a lot of attention in the physics literature of the last several years as simple toy models remarkably capturing many features expected of full-fledged quantum gravity. I will review some basics of the DSSYK model, outlining its solution via chord techniques and explaining how the model is governed by quantum group symmetry. Then I’ll explain the basics of quantum homogeneous spaces, and show how the bulk dual of the DSSYK is constructed in this framework. If time permits, I will also discuss relations with the other recent approaches to the bulk dual of the DSSYK.

**Emilio Trevisani **(LPTHE) |** Parisi-Sourlas supersymmetry, random fields and the uplift**

The problem of quenched disorder is very important but notoriously hard. In 1979 Parisi and Sourlas proposed a conjecture about the critical behavior of models with random field type of disorder. The conjecture states that 1) such models have emergent supersymmetry and 2) that supersymmetry allows to describe them in terms of models in two less dimensions. I will review the conjecture and explain some recent developments on the subject. Also I will discuss how to use this supersymmetry to uplift conformal field theories to higher dimensions.

###### 20 March 2024, Leuven

**Damián Galante **(King’s Coll. London) | **Gravitational observatories** Motivated by the necessity to understand cosmological spacetimes from a quasi-local perspective, I will discuss timelike boundaries in general relativity and the initial boundary value problem. I will comment on issues with the standard Dirichlet problem and discuss a conformal variation of it, that is conjectured to be well-posed. Using these boundary conditions, both dynamical and thermodynamical aspects of the problem with and without a cosmological constant will be discussed.

**Ana Alonso Serrano **(Potsdam) |** Thermodynamics as a tool for (quantum) gravitational dynamics**

I present a review of concepts of thermodynamics of spacetime and the gravitational dynamics encoding in it, discussing also the recovery of Weyl transverse gravity instead of General Relativity. Then, I present a formalism to analyze low-energy quantum gravity modifications in a completely general framework based on the thermodynamics of spacetime. For that purpose, I consider quantum gravity effects via a parametrized modification of entropy by an extra logarithmic term in the area, predicted in most of the different approaches to quantum gravity. These results provide a general expression of quantum phenomenological equations of gravitational dynamics. Furthermore, I outline the application of the modified dynamics to particular models, such as cosmology and its predictions.

###### 13 March 2024, Brussels

**Dalimil Mazac **(IPhT, Saclay) | **Constructive CFTs and hyperbolic geometry** One of the main lessons of the modern conformal bootstrap is that higher-dimensional CFTs are rigid mathematical structures that can be plausibly isolated using a set of precise axioms. However, very little is known about how these structures can be explicitly constructed. In my talk, I will explain why hyperbolic manifolds are an excellent toy model for the problem of constructive CFT. Indeed, the spectra of hyperbolic d-manifolds satisfy the same bootstrap equations as CFTs in (d-1) dimensions. These spectra exhibit quantum chaos and enjoy deep links to number theory. Furthermore, ongoing work by mathematicians proves that the spectra of hyperbolic manifolds can indeed be fully isolated by the conformal bootstrap equations. Based on work with J. Bonifacio, P. Kravchuk and S. Pal.

**Martin Cederwall **(Chalmers Univ.) |** Extended geometry with infinite-dimensional structure groups**

I review some aspects of extended geometry, with focus on the local symmetries and the connection to tensor hierarchy algebras (THA’s). I discuss briefly different forms of the dynamics, in particular the teleparallel one, which has a natural cohomological interpretation related to the THA’s. Finally, I discuss some lessons about infinite-dimensional structure groups, which appear when the number d of external dimensions is 2 or smaller.

###### 6 March 2024, Leuven

**Ohad Mamroud **(Weizmann Inst.) | **From Chaos to Integrability in Double Scaled SYK** The talk will be about a thermodynamic phase transitions between integrable and chaotic dynamics. First, I will briefly review the chaotic SYK model and its double scaled limit, where it is described by chord diagrams. I will then present a path integral formalism by coarse graining over the diagrams. This will allow us to study a deformation of the model by an integrable Hamiltonian, and to show that the system has two distinct phases: a chaotic one and a quasi-integrable one, which are separated by a first order transition.

**Federico Capone **(Jena) | **Superrotations, tales in various dimensions**

Superrotations of 4D asymptotically flat spacetimes extend the standard BMS group, can be used to derive soft scattering theorems, and are pivotal in the realization of Celestial CFT (CCFT), an exotic 2D CFT putatively dual to 4D gravitational theories in AF spacetimes. The first tale proposes an intrinsic Flat Holography approach – using superrotations – to holographically compute CCFT twist field correlators and Renyi/Entanglement Entropies. This part is based on work soon to appear. The second tale changes gear and discusses first the general asymptotic structure of Ricci flat gravity with null boundary in any dimension and, then, its reduction to the simplest example of a phase space in 6D with supertranslation and superrotation charges renormalized in a local and covariant way. This results in the first detailed proof of the relationship between soft theorems and supertranslations/superrotations in 6D (applicable to all even dimensions).

###### 28 February 2024, Brussels

**Johan Henriksson **(IPhT, Saclay) | **Code CFTs, averaging, and holography** Recent advances indicate that 3d gravity may be dual not to a single CFT but to an average over an ensemble of CFTs. In this talk I will discuss CFTs deriving from error-correcting codes. Such codes have been studied and classified by discrete mathematicians for decades, and give rise to CFTs via a lattice construction. Error-correcting codes, and therefore code CFTs, come in natural discrete ensembles which provide explicit expressions for averaged observables. The main result is that for various constructions of code CFTs, it is possible to give a holographic interpretation of the averaged partition function as a Poincaré sum corresponding to a sum over bulk geometries, providing the ground for several interesting new directions.

**Riccardo Gonzo **(Edinburgh) | **Gravitational bound waveforms from amplitudes**

We will develop a formalism to study the gravitational waveform emitted during the inspiral phase of the dynamics of compact objects (black holes, neutron starts) using the effective field theory approach with a point particle description. First, we consider the scattering setup for the two-body problem where a natural on-shell relation between waveforms and amplitudes can be established in the classical limit. As a concrete example, focusing on the case of two Kerr black holes, we derive the time-domain waveform at leading order in the Post-Minkowskian expansion and at quartic order in the spin by using S-matrix analyticity arguments to bypass the conventional observable phase-space integration. We will then derive a new surprising on-shell map between scattering and bound waveforms, which is inspired and confirmed by Post-Newtonian calculations with the standard time-domain multipoles, and we will show that a resummation of the perturbative series is required to make contact with phenomenological waveform models.

###### 21 February 2024, Leuven

**Yixuan Li **(Munich) | **Holography for KKLT: The Anatomy of a Flow** Flux compactifications that give three- or four-dimensional Anti-de-Sitter vacua with a parametrically-small negative cosmological constant are supposed to be ubiquitous in String Theory. However, the 1+1 and 2+1 dimensional CFT duals to such vacua should have a very large central charges and rather unusual spectra. Furthermore, there are various swampland conjectures that such vacua should not exist. In this talk, I will explain how we construct brane configurations that source the would-be AdS vacua coming out of these flux compactifications, and identify certain UV AdS geometries that these systems of branes source. These place upper bounds on the possible values of the cosmological constants of the scale-separated AdS vacua.

**Giuseppe Policastro **(Geneva) | **Matrix Quantum Mechanics and quantum averaging of JT gravity**

I will discuss the matrix quantum mechanics with potential corresponding to an arbitrary spectral curve. This can be seen as a generalization of the duality between JT gravity and a particular matrix integral. Using the recently developed techniques of quantum generalised hydrodynamics, the effective theory of the eigenvalue density fluctuations is a simple 2D free-boson BCFT on a curved background. The ensemble average over random matrices then corresponds to a quantum expectation value. Using this formalism we reproduce non-perturbative results for matrix integrals (the ramp and the plateau in the spectral form factor). We also compute the entanglement between eigenvalues, matching a previous result by Hartnoll and Mazenc for the c = 1 matrix model and extending it to the general case. The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory.

###### 14 February 2024, Brussels

**David Berenstein **(Santa Barbaran, Amsterdam) | **The view of a point: Wigner-Inonu contractions and the flats space limit of AdS scattering** I will describe how to consider the flat space limit of scaterig in AdS relative to a point (where scattering occurs). The kinematics is related to the Wigner-Inonu contraction. In particular, I will discuss how to take the proper limits of wave functions in AdS (times extra dimensions) to understand a notion of in states and out states and how a scattering amplitude should be conceived. This will make use of the embedding formalism, where the description of these wave functions is simple. I will show how these wave functions are related to other constructions in AdS/CFT and suggest how the Mellin parameters of these other setups arise from integral representations of the wave functions in terms of Schwinger parameters.

**Xavier Bekaert **(Tours) | **Holographic realisation of Carrollian conformal scalars**

The singleton is a remarkable unitary representation of the conformal algebra, which was first investigated by Dirac in the sixties, and whose bulk/boundary description in the seventies by Flato and Fronsdal is sometimes considered as a precursor of the AdS/CFT correspondence. The flat limit of the singleton on AdS spacetime is shown to provide the bulk dual, in Minkowski spacetime, of the Carrollian conformal scalar field living at null infinity.

###### 7 February 2024, Leuven

**Valentin Reys **(IPhT, Saclay) | **Logarithmic corrections in AdS/CFT** In this talk, I will review the heat kernel formalism and explain how it can be used to compute logarithmic terms in the semi-classical expansion of supergravity observables due to one-loop effects. When applied to holographic Kaluza-Klein supergravity theories with a known spectrum, this method produces results that can be matched to the logarithmic terms in the large N expansion of the dual CFT observables. When available, our results are also compatible with one-loop computations in 11d supergravity and in supergravity localization. Reverting the logic, a mild assumption on the coefficient of log N terms in CFT observables yields strong constraints on the spectrum of arbitrary gravity theories in order for them to be compatible with AdS/CFT at the quantum level.

**Denis Karateev **(Geneva) | **Trace anomalies and the dilation-graviton amplitude**

We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to (∆c − ∆a) along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate (∆c − ∆a) to spinning massive states in the spectrum of the QFT. We test our predictions on a simple example of a massive free scalar. We discuss possible applications.

###### 31 January 2024, Brussels

**Jakub Vošmera **(IPHT Saclay) | **Topological defect lines and tensionless holography** Topological defect operators proved to be an indispensable tool in understanding and generalizing the concept of symmetry in quantum field theory. In this talk, we investigate realizations of topological defect

lines in some concrete examples of holographic 2d CFTs. In the particular case of a symmetric product orbifold CFT of four free fermions and bosons, we identify the AdS3 tensionless string worldsheet duals of various topological defect configurations in the 2d spacetime CFT.

**Caroline Jonas **(KUL) | **Stability of new axion-dilaton wormholes**

Euclidean wormhole are instanton-like solutions connecting two different asymptotic spacetime. Their contribution to the Euclidean path integral would mediate topology changes in 4D quantum gravity, but their existence is related to numerous puzzles, from non-unitary processes to inconsistencies with the AdS/CFT correspondence, and has been debated for more than 30 years now. In this talk, I will report on the finding of new axion-dilaton Euclidean wormhole solutions when the dilaton is massive and on the perturbative stability of these solutions, as well as the stability of axion-massless dilaton wormhole solutions in general (Giddings-Strominger wormholes). Massless dilaton wormholes are always stable in the homogeneous sector, and so are the lowest dilaton solutions in the massive dilaton case. In the latter case we observe the appearance of an additional negative mode when several branches of solutions develop. Finally I will discuss the implications of these results in light of the above-mentionned paradoxes.

###### 13 December 2023, Brussels

**Hynek Paul **(KUL) | **Bootstrapping holographic correlators – an overview** I aim to give an accessible review of the recent progress in constructing correlation functions of half-BPS operators in the supergravity limit. Focussing mostly on 4pt-functions in N=4 SYM, dual to scattering of supergravitons in AdS5 x S5, I will illustrate the analytic bootstrap programme at tree-level and one-loop order.

**Kurt Hinterbichler **(Case Western Reserve University) | **Shift Symmetries in (A)dS **

I will discuss generalizations of shift symmetries, galileon symmetries, and extended galileon symmetries to (A)dS space and to higher spin. These symmetries are present for fields with particular masses, and are related to partially massless symmetries. I will discuss some of the properties of fields with these symmetries and their invariant interactions, including their group theoretic origin, the existence of certain fully interacting examples, and speculations on possible generalizations to higher spin theories.

###### 6 December 2023, Leuven

**Aleix Gimenez **(IHES) | **Bootstrapping defect two-point functions in N=4 SYM and 6d (2,0) theories**

In recent years, there has been significant progress in our ability to compute correlation functions in holographic CFT. While the focus has primarily centered on correlation functions of local operators, this merely scratches the surface of all observables in these theories. The reason is that, due to their string theory origin, holographic CFTs are equipped with a vast array of extended objects — D-branes, long fundamental strings, M-branes, and more. Motivated by this lack of results, the present work initiates the study of correlation functions that mix local and extended operators, focusing on the simplest one: the correlator of two half-BPS local operators and one half-BPS extended operator. We propose a robust bootstrap algorithm, enabling the computation of these correlators in the tree-level approximation. Applying this algorithm to N=4 SYM and the 6d (2,0) theory yields closed-form expressions for the correlators, that are surprisingly simple in Mellin space. Talk based on: 2306.11896, 2310.19230.

**Alexandre Serantes **(Ghent) | **Bootstrapping relativistic transport from causality** As an effective field theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. In this talk, I will explain how microscopic causality leads to a universal convex geometry in the space of transport coefficients, the hydrohedron, which contains every consistent theory of relativistic transport. I will analytically construct cross-sections of the hydrohedron corresponding to bounds on transport coefficients that appear in sound and diffusion modes for theories without stochastic fluctuations. Based on 2212.07434 and 2305.07703.

###### 29 November 2023, Brussels

**Lorenzo Di Pietro **(INFN, Trieste) | **BCFT One-Point Functions of Coulomb Branch Operators**

I will discuss a method to compute the one-point functions of chiral primary operators in 4d N=2 SCFTs with ½ BPS boundary conditions. A SUSY identity relates these correlators to derivatives of the hemisphere partition function, adapting to the boundary case the known method to compute chiral/antichiral two-point functions. This requires to take appropriate care of certain boundary terms in the Ward identities. I will then show the localization formulas that can be used to derive exact results for these one-point functions. As an explicit example, I will focus on the case of super Maxwell theory coupled to a 3d N=2 SCFT on the boundary.

**Robie Hennigar **(ICC, Barcelona) | **Charged Quantum Black Holes from Holography** Holography is a powerful tool for understanding properties of strongly coupled quantum field theories on curved space-times. In this talk, I begin by discussing holographic set-ups involving a dyonic, localized defect in a conformal field theory on (conical) AdS$_3$, Minkowski space, and BTZ black holes. The bulk duals of these configurations can be constructed analytically and used to study the properties of the CFTs on these fixed backgrounds. I then show how, by utilizing brane-world holography, the non-linear back-reaction of the quantum fields can be accounted for. The result is a new class of charged three dimensional quantum black holes that differ in notable ways from the classical charged BTZ black hole. I discuss properties of the solutions, such as their thermodynamics and extremal limits. This is based on forthcoming work with Ana Climent and Roberto Emparan.

###### 22 November 2023, Ghent

**Cristoforo Iossa **(Geneva) | **Black hole bulk-cone singularities**

Holographic correlators exhibit singularities associated with null geodesics propagating in an emergent bulk geometry. We analyze singularities of the thermal response function dual to propagation of waves on the AdS-Schwarzschild black hole background, and derive the analytic form of the leading singularity dual to a bulk geodesic that winds around the black hole. To perform the computation analytically we express the two-point correlator as an infinite sum over Regge poles. We then check our predictions numerically, and argue that these singularities could serve as a target for simulations of black hole-like geometries in table-top experiments.

**Lorenz Eberhardt **(Amsterdam) | **The Virasoro Minimal String** I will introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral, which provides the holographic description. The worldsheet theory consists of Liouville CFT with central charge c\ge 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, which gives the theory its name. The talk is based on joint work with Scott Collier, Beatrix Mühlmann and Victor Rodriguez.

###### 15 November 2023, Brussels

**Flourent Baume **(Hamburg U.) | **(Higher-)-spinning in the holographic Swampland**

The study of low-energy theories that can be embedded into string theory has led to a number of proposals about the nature of quantum gravity. Via holography, they should also have implications for Conformal Field Theories. In this talk, I will discuss the CFT Distance Conjecture, which posits that at infinite-distance points of a conformal manifold, there is an infinite tower of conserved higher-spin currents, indicating that a sector of the CFT becomes free, and vice versa. After motivating it from the gravity side and through examples, I will argue that under a natural set of assumptions, such as unitarity and the existence of an energy-momentum tensor but without requiring the presence of supersymmetry, it is possible to prove that all points with such a tower of higher-spin currents are indeed at infinite distance.

**Shira Chapman **(Ben Gurion U.)| **Energy Reflection and Transmission at 2D Holographic Interfaces** Scattering from conformal interfaces in two dimensions is universal in that the flux of reflected and transmitted energy does not depend on the details of the initial state. In this talk, I will present two gravitational calculations of the energy reflection and transmission coefficients for interfaces with holographic duals. I will first consider a thin-brane holographic toy model which is often used in the context of entanglement islands and black hole evaporation. I will demonstrate that the result for the reflection coefficient there depends monotonically on the tension of the brane. I will then extend the calculation to smooth domain-walls in 3-dimensional gravity. As an application, I will compute the transmission coefficient of a Janus interface in terms of its deformation parameter. I will demonstrate that both results obey bounds derived from the ANEC in conformal field theory.

###### 8 November 2023, Mons

**Blagoje Oblak **(ULB) | **Anisotropic Quantum Hall Droplets**

This talk is devoted to 2D droplets of free electrons in a strong magnetic field, placed in an arbitrary confining potential. I show that semiclassical methods in the lowest Landau level yield near-Gaussian energy eigenstates localized on level curves of the potential, implying explicit formulas for local many-body observables in the thermodynamic limit. In particular, correlations along a droplet’s edge are long-ranged, in accordance with the 1D chiral conformal field theory description of low-energy dynamics. This notably involves inhomogeneous correlations and position-dependent guiding centre velocities, but still results in a homogeneous theory thanks to remarkable cancellations between the radial and angular dependencies of eigenfunctions. Finally, I describe realistic microwave absorption experiments that probe the detailed shape of a droplet without resorting to local imaging.

**Antoine Bourget **(IPhT)|** Why Symplectic Singularities**

In the past decade, a kind of geometric space known as symplectic singularities have become a popular topic for an increasing community of physicists and mathematicians. My goal in this presentation is to explain to you the reasons for this sudden interest, and try to convey the delicate beauty of this field.

Within the context of supersymmetric theories, they have incarnations as hyperKähler quotients, Higgs branches, Coulomb branches, they serve as a tool in the study of SCFTs, allow to explore RG flows and deformations, and are connected to vertex operator algebras. In this review talk, I will recall the basic definitions and examples, and mention a few very recent advances and open problems.

**Ana-Maria Raclariu **(University of Amsterdam)|** Entanglement, soft modes and celestial CFT**

In this talk I will revisit the calculation of entanglement entropy in free Maxwell theory in 4-dimensional Minkowski spacetime. Weyl invariance allows for this theory to be embedded inside the Einstein static universe. Future null infinity can be regarded as the union of Cauchy slices inside the future Milne patches (denoted L and R) of two Minkowski geometries related by a conformal inversion. I will show that the Maxwell vacuum state decomposes as the thermofield double state of conformal primary modes supported inside the L and R patches and related by a conformal inversion. I will comment on the relation between inversions and shadow transforms. I will conclude by discussing the soft sectors associated with the two patches. In particular, I will demonstrate that conformally soft mode configurations at the entangling surface, or equivalently correlated fluctuations in the large gauge charges of the two Milne patches, give a non-trivial contribution to the entanglement entropy across a cut of future null infinity.

###### 25 October 2023, Leuven

**Alex Belin **(Milan Bicocca U.) | **How Non-local is Quantum Gravity?**

Locality is a powerful property of quantum field theory and implies that information can be strictly localized in regions of space, and is completely inaccessible from far away. On the other hand, the holographic nature of quantum gravity suggests that the theory is ultimately non-local and that information can never be localized deep inside some spacetime region, but rather is always accessible from the boundary. This is meant to hold as a fully non-perturbative statement, but the fate of locality in G_N perturbation theory is unclear. To investigate locality in quantum gravity, an important first step is to define candidate local operators. The challenge is that to be diffeomorphism-invariant, i.e. to respect the gravitational Gauss law, such operators must be gravitationally dressed which usually makes them non-local. In this talk, I will discuss the incarnation of this problem in the context of AdS/CFT and propose a set of operators which appear to be local to all orders in G_N perturbation theory. Such operators can only be defined around sufficiently complicated CFT states, for reasons that I will explain. I will also comment on the connection of this framework to the introduction of an observer in de Sitter space.

**Fien Apers **(Oxford U.)|** Exploring Holographic Duals of Scale-Separated AdS Vacua**

This talk aims to investigate scale-separated AdS vacua in string theory by studying their potential holographic duals, with a specific focus on the DGKT vacua. We will also discuss a bottom-up approach for constructing the brane dual given an AdS effective field theory with large flux. Based on work in progress with Miguel Montero and Irene Valenzuela.

###### 18 October 2023, Brussels

**Silviu Pufu **(Princeton) | *Two approaches to adjoint QCD2*

In this talk, I will discuss the 2d SU(N) gauge theory coupled to an adjoint Majorana fermion using two approaches. First, I will describe the computation of the spectrum at finite N using Discretized Light-Cone Quantization. Then, for the N=2 case, I will introduce a Hamiltonian lattice model that can also be used to compute the spectrum as well as other observables using analytical and numerical techniques.

**Andrew Rolph **(University of Amsterdam and Vrije Universiteit Brussel) | **Page curves and replica wormholes from random Hamiltonians**

What is the underlying mechanism for the late-time purification of Hawking radiation from evaporating black holes? Which properties of gravity are important and which are not? In this talk I will show how to capture both the non-unitary Page curve and density matrix-connecting contributions that restore unitarity in a toy quantum system with random dynamics. The motivation is to find the simplest dynamical model that captures this aspect of gravitational physics. In the model, the Hamiltonian obeys random matrix statistics within microcanonical windows, the entropy of the averaged state gives the non-unitary curve, the averaged entropy gives the unitary curve, and the difference comes from matrix index contractions in the Haar averaging that connect the density matrices in a replica wormhole-like manner.

###### 11 October 2023, Leuven

**Bastien Duboeuf** (ENS de Lyon) | **Kaluza-Klein Spectrometry and Cubics Couplings using Exceptional Field Theory**

I will discuss recent progress in our ability to compute the Kaluza-Klein spectrum through the utilization of Exceptional Field Theory (ExFT). To provide a comprehensive understanding of our findings, I will start with an overview of ExFT, which is necessary for comprehending the outcomes we have achieved. This encompasses our ability to compute spectra that goes beyond consistent truncations, as exemplified by our work on 11D supergravity within the AdS4 × S7 background, where S7 represents a squashed sphere. Additionally, I will delve into novel underlying structures we have uncovered and outline how we can extend our prior results to encompass any solution featuring a sphere with a coset representation. To conclude, I will demonstrate how ExFT techniques can be expanded to investigate not only spectra but also the cubic couplings within supergravity theories.

**Ilka Brunner** (Munich U.) | **Truncated affine Rozansky Witten models as extended defect TQFT**

I will discuss how to construct extended topological field theories associated to Rozansky Witten models with affine target manifolds. For our construction, we will systematically exploit the cobordism hypthesis and construct for example state spaces associated to 2-dimensional surfaces dressed with arbitrary defect networks.

###### 4 October 2023, Brussels

**Dominik Neuenfeld** (Julius-Maximilians-Universität Würzburg) | **Consistency of Double-Holography from the Bottom Up**

Karch-Randall-Sundrum (KRS) braneworlds have recently enjoyed a resurgence in popularity as they offer insights into the physics of black hole evaporation, particularly in higher dimensions. Since no well-controlled derivation of these model from string theory or supergravity is available, open questions remain about the consistency and existence of these models. In this talk, I will discuss aspects of the consistency of these models from the “bottom up”.

A particular challenge to the consistency of KRS braneworld models comes from the fact that they seemingly allow for superluminal signaling. I will argue that as long as the brane description is treated as an effective theory, causality violations are not visible above the associated cutoff length scale. In this context, I will discuss several criteria that define regions outside which time evolution within the effective theory is thought to break down and compare them. All criteria exclude regions which could naively be affected by superluminal signaling.

KRS models also allow for higher derivative couplings on the brane, so-called DGP terms. Using properties of the dual CFT, I will show how certain values for the couplings of such terms can be ruled out for branes in three dimensional bulk spacetimes, placing some of those models in the swampland.

**Christopher Couzens** (Oxford University) | **M5-branes wrapped on discs**

Given an SCFT one can obtain, under certain conditions, new SCFTs by compactifying the theory on compact spaces. This gives an RG flow across dimensions and in holography corresponds to a background interpolating between different dimensional AdS vacua. We will focus on the class of four-dimensional N=2 SCFTs, known as theories of class S, obtained by compactifying the various 6d N=(2,0) SCFTs living on M5-branes on two-dimensional surfaces. There are two main classes of two-dimensional surfaces on which we may compactify, depending on the types of punctures (regular or irregular) of the Riemann surface. We will discuss recent work on the holographic duals of these theories with irregular punctures which are of Argyres—Douglas type.