# Joint Belgian hep-th seminars: academic year 2021-2022

###### 1 June 2022, Brussels

** Cliff Burges **(Perimeter Institute and McMaster U.) |

**RG Modulus Stabilization, de Sitter vacua and the inflationary eta problem**This talk describes a new mechanism for stabilizing moduli in supergravity theories without leaving the domain of perturbative control. The only required nonperturbative information (as required by the ‘Dine-Seiberg’ problem) comes from the standard renormalization-group resummation of leading logarithms. The resulting potential is naturally minimized for exponentially large moduli even given input parameters that involve only hierarchies that are O(10). The resulting compactifications generically break supersymmetry and de Sitter vacua are relatively easy to achieve without the usual uplifting problems encountered in other stabilization methods (like KKLT or LVS scenarios). Variations on the theme lead to inflationary scenarios for which the size of the stabilized moduli differ significantly before and after inflation and so provide a dynamical mechanism whereby inflationary scales are much larger than late-time physical (e.g. supersymmetry breaking) scales. When applied to warped D3-D3 inflation this stabilization mechanism evades the eta-problem that usually prevent justify slow roll in this scenario.

** Rob Leigh **(University of Illinois) |

**Towards a Quantum Corner Theory of Gravity**In this talk I will review recent work on identifying and studying a universal symmetry of diffeomorphism invariant classical theories. This symmetry was originally identified by studying the diffeomorphism Noether charges which have support on codimension-2 embedded (or immersed) surfaces (‘corners’) in a classical space-time manifold M. This symmetry, which we now refer to as the universal corner symmetry (UCS), is the maximal closed subalgebra of Diff(M) that Noether charges can support. This statement is completely general, making no reference to any particular geometry or choice of coordinates. It is interesting to contemplate this symmetry as an underlying structure of a quantum theory of space-time. As such, a study of its representation theory is of central interest. I will report on a careful study of the coadjoint orbits of the universal corner symmetry. One finds that there are various orbits which we identify as corresponding to corners that support certain ideals of the UCS; the two principle cases are generic ‘finite-distance’ corners (that classically can be interpreted as boundaries of subregions) and ‘asymptotic’ corners. In the latter case, the subalgebra is precisely BMSW. If time permits, I will describe a complete geometrization of this story in terms of an Atiyah Lie algebroid. This may suggest that quantum gravity can be considered as a gauge theory defined, not on space-time, but on a corner.

###### 25 May 2022, KUL

**Mahdi Godazgar **(Queen Mary U. of London) | **Dual gravitational charges**

I will explain how one can derive dual asymptotic gravitational charges using the first-order tetrad formalism. I will then explain why such dual charges are important.

**Matt Roberts **(Imperial College London) | **Elastically deformed graphene and curved space Dirac: a cautionary tale**

Graphene has many (in)famous features, two of which are: quasiparticles which take the form of massless Dirac fermions, as well as remarkable tensile strength (especially considering it is a one atom thick membrane!). Many people (including myself) have used it as experimental motivation for studying the 2+1D QFTs in curved space. Under elastic distortions, the quasiparticles couple to a gauge field proportional to strain, and it is often stated that we can model distorted graphene via a Dirac field coupled to a background magnetic field. We demonstrate that this is genetically not true, as the magnetic field is at the lattice scale, ruining our gradient expansion. In the perturbation regime the only consistent truncation of a Dirac equation is one in a flat cartesian metric. This raises the question of what precisely the continuum limit of elastically deformed graphene is.

###### 18 May 2022, Brussels

**Noppadol Mekareeya **(INFN Milano Bicocca) | **Recent Developments in Argyres-Douglas theories**

Argyres-Douglas (AD) theories constitute an infinite class of 4d N=2 superconformal field theories with a number of interesting properties. A distinctive feature of these theories is the presence of Coulomb branch operators of fractional dimension. In this talk, we discuss several new aspects of such theories, including their conformal manifolds, structures of the Higgs branch, as well as the 3d gauge theories that arise from dimensional reduction on a circle. We present a number of dualities between 3d N=4 gauge theories coming from the latter. The dynamical consequences of one-form symmetries in various AD theories are also discussed in the talk.

**Dave Tennyson **(Imperial College London) | **Topological strings at 1-loop from double complexes**

The topological A/B-model have been important tools for studying both string theory and the geometry of Calabi-Yau manifolds. They provide both new geometric invariants of the Calabi-Yau, as well as calculating certain terms in the effective theory of string theory. While topological strings on other special holonomy manifolds have been postulated, they are far less understood. In my talk, I will examine the topological string on G2 and Spin(7) manifolds from the target space perspective. I will show that any special holonomy manifold has a double complex which generalises the Dolbeault complex of Calabi-Yau manifolds and provides the natural candidate for the BRST complex of the topological string. Through this, I will be able to conjecture the cohomology of operators and the 1-loop partition functions of the G2 and Spin(7) topological strings.

###### 11 May 2022, UMONS

**Axel Kleinschmidt **(AEI Potsdam) | **The most complicated way of writing D=11 supergravity**

Exceptional field theory based on the exceptional group E_n is a way of combining aspects of supergravity in a duality covariant way. It can make the Cremmer-Julia E_n symmetry in 11-n dimensions manifest but can also be seen as a way of rewriting the theory in eleven dimensions, breaking the symmetry in the course of doing so. I will review recent results where this idea is taken to the limiting case with Kac-Moody symmetry E11, highlighting interesting representation-theoretic aspects. Based on work with Guillaume Bossard and Ergin Sezgin

**Alejandra Castro **(UvA Amsterdam) | **Near AdS_2 spectroscopy**

In this talk, I will describe holographic properties of near-AdS_2 spacetimes that arise within spherically symmetric configurations of N=2 4D supergravity, for both gauged and ungauged theories. These theories pose a rich space of AdS_2xS^2 backgrounds, and their responses in the near-AdS_2 region are not universal. I will show that the spectrum of operators dual to the matter fields, and their cubic interactions, are sensitive to the properties of the background and the theory it is embedded in. The properties that have the most striking effect are whether the background is BPS or non-BPS, and if the theory is gauged or ungauged. The resulting differences will have an imprint on the quantum nature of the microstates of near-extremal black holes, reflecting that not all extremal black holes respond equally when kicked away from extremality

###### 4 May 2022, KUL

**Daniel Brennan **(Chicago U.) | **Line Operator Quantum Numbers and Anomalies**

In this talk we will describe a new mechanism for studying anomalies of discrete symmetries in 4D gauge theories. This mechanism simply requires flowing to a pure abelian gauge theory where the anomaly can be computed in terms of the quantum numbers of electric and magnetic line operators. We demonstrate our program by computing the anomaly in SU(2) QCD with 2N fundamental fermions and show that for certain N, there is a new class of anomaly that exists for arbitrarily large N.

**Prem Kumar **(Swansea U.) | **Entanglement evolution and islands in the stream of Hawking radiation**

In this talk I will describe aspects of island saddles that contribute to time evolution of measures of entanglement in the Hawking radiation emitted by slowly evaporating black holes coupled to nongravitating radiation baths. In the adiabatic limit multiple island saddles can be identified via a simple prescription in terms of the images of islands in the stream of the Hawking radiation. I will describe how quantum extremal surfaces and the island prescription applied to the JT gravity framework reproduces intricate features of entropy evolution in free fermion BCFT.

###### 20 April 2022, Brussels

**Niccolò Cribiori **(Munich, Max Planck Institute for Physics) | *Binding and freeing scale separation in 4D and 10D*

The existence of a separation of scales between the four observed spacetime dimensions and the yet unobserved additional ones is a minimal requirement for (string) phenomenology. Explaining the origin of this property at the theoretical level is an open problem. In the fist part of the talk, I will present a general argument excluding scale separation in supersymmetric anti de Sitter vacua of N=2,8 supergravity as a consequence of the weak gravity conjecture. I will also explain how N=0,1 vacua can evade such an argument. Indeed, scale separated N=1 anti de Sitter vacua are known in massive type IIA supergravity. In the second part of the talk I will revisit these constructions in ten dimension and show how to overcome some possible criticisms, while preserving scale separation. In particular, I will give evidence for the existence of scale separated anti de sitter vacua in massless type IIA supergravity, both at weak and strong coupling, while going a step beyond the smeared approximation.

**Nicolas Kovensky **(IPhT, Saclay) | *Heavy-Light correlators at the end of the world(sheet)*

Light probes interacting with heavy bound states such as black holes give rise to interesting observables containing valuable dynamical information. Recently, a family of black hole microstates was shown to admit an exact string worldsheet description. In this talk I will start by constructing the physical vertex operators of these models, and derive their form in the low-energy AdS3 limit. Then, I will show how to use them to compute an extensive set of novel heavy-light correlators in these backgrounds. A subset of these provide the first match between worldsheet correlators in black hole microstates and the holographically dual conformal field theory. I will further present conjecture a closed formula for heavy-light correlators with an arbitrary number of light insertions. As an application, these results can be used to compute the analogue of the Hawking radiation rate for these microstates.

###### 30 March 2022, Brussels

**Pierre Vanhove **(IPhT, Saclay) | *Classical gravitational observables from quantum amplitude methods*

We describe the application of modern amplitude techniques to the analytic evaluation of classical gravitational observables. These methods from quantum scattering amplitudes have led to a new point-of-view on the computation of the coalescence of compact binaries in the classical post-Minkowskian expansion. This approach applies to any effective field theory of gravity, and provide a theoretical framework for investigating gravitational physics beyond Einstein’s theory of gravity.

**Juan Hernandez **(VUB) | **Quantum extremal islands made easy**

We review the easy island setup, in which quantum extremal islands naturally arise as a connected/disconnected phase transition in the RT surfaces of two disconnected regions. First, we introduce the model in general dimensions and overview some properties of entanglement entropy and holographic complexity in the island phase. We then turn our attention to the three dimensional case with a bulk BTZ black hole and a Randall-Sundrum brane and we consider including an intrinsic JT gravity action on the brane.

###### 23 March 2022, KUL

**Dionysios Anninos **(King’s College London) | *Comments on Euclidean de Sitter*

We explore the cosmological version of Euclidean black hole thermodynamics, namely the gravitational path integral over compact manifolds, in various dimensions. In general dimension we discuss the thermodynamic picture of the sphere path integral in terms of the quantum field theoretic Hilbert space in a Lorentzian de Sitter. In lower than four dimensions we discuss the availability of exact results.

**Bobby Acharya **(ICTP Trieste and King’s College London) | **Grand Unification and the physics of some G2-holonomy and SU3-holonomy singularities**

We will begin by reviewing the geometric unification of fundamental interactions according to M theory, where particular kinds of singularities play a special role. Then we will present recent results (w/ L. Foscolo) describing how very particular G2-holonomy conical singularities give rise to antisymmetric GUT representations. Then, if time permits, we interpret a class of non-Abelian Calabi-Yau threefold orbifolds in terms of 5d superconformal theories.

###### 16 March 2022, online talk

**Daniel Klaewer **(Hamburg U.) | **Membrane Limits in Quantum Gravity**

In the context of the swampland program, any infinite distance limit in the moduli space of quantum gravity is expected to be governed by an infinite tower of exponentially light states. More precisely, the emergent string conjecture posits that the dominant tower is always either a tower of KK states or string excitations, amounting to a universality statement about infinite field displacements. In the first part of my talk, I will review the statements of and arguments for these conjectures. Furthermore, I will give an overview over the many non-trivial tests that the emergent string conjecture has passed, especially in the vector multiplet moduli space of N=2 compactifications of string theory. The second part of the talk will be concerned with a challenge for the emergent string conjecture that arises in the hypermultiplet moduli space. M-theory compactified on a Calabi-Yau threefold classically allows for limits where the relevant light object is not a string or KK tower, but a membrane. I will argue that such limits are obstructed in the instanton-corrected moduli space.

###### 9 March 2022, online talk

**Gary Horowitz **(UC Santa Barbara) | **A new type of extremal black hole**

I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.

###### 2 March 2022, online talk

**Mathew Bullimore **(Durham U.) | **Symmetries and ‘t Hooft anomalies of 3d N = 4 SCFTs**

I will discuss aspects of higher-form and higher-group symmetries and their ‘t Hooft anomalies in 3d N = 4 SCFTs. Time permitting, I will comment on how these symmetries are encoded in a generalisation of Higgs and Coulomb branch moduli spaces to moduli stacks.

###### 23 February 2022, online talk

**Irina Aref’eva **(Steklov Math. Inst., Moscow) | *Black hole explosions?*

The problem of complete evaporation of Schwarzschild black holes raised by Hawking is that one has an explosion of the temperature $T=1/8\pi M$ for vanishing black hole mass M. We consider the Reissner-Nordstrom black hole and study under which conditions the complete evaporation of black holes without blow-up of temperature is possible. We describe curves on the surface of state equations such that the motion along them provides complete evaporation. Under the assumption of slow evaporation, we estimate the time dependence of the entanglement entropy of radiation on island configurations along these curves.

###### 16 February 2022, online talk

**Lionel Mason **(Oxford U.) | **The twistor origin of celestial W-infinity symmetry**

This talk will first set out to explain how the loop algebra of the the w-infinity algebra, understood as the area-preserving diffeomorphisms, acts on the space of Self-dual gravitational phase space via Penrose’s twistor correspondence. Using a recently introduced sigma model, we show how the algebra can be expressed on the celestial sphere via a sigma model with the twistor space as target in such a way as to express the w-infinity algebra in terms of the soft algebra recently found by Strominger, based on earlier joint work. This is based on joint work with Tim Adamo and Atul Sharma https://arxiv.org/abs/2110.06066 and https://arxiv.org/abs/2103.16984.

###### 9 February 2022, online talk

**Kristan Jensen** (Victoria U.) | **Large N fractons**

In this talk I will discuss two aspects of continuum field theories of fractons. These models have been of recent interest to condensed matter and high energy theorists. On the one hand they are candidates for new phases of quantum matter, and on the other, they have features which seem impossible to describe in continuum field theory, including quasiparticles of restricted mobility and a ground state degeneracy which depends sensitively on the ultraviolet.

The two aspects I will discuss are (i.) some soluble interacting large N versions of these models, and (ii.) the coupling of these models to a spacetime background, useful for obtaining Ward identities for response functions. Our large N results show in detail the importance of interactions, and how a careful treatment of the path integral in continuum field theory can reproduce the exotic features mentioned above.

###### 2 February 2022, online talk

**Thomas Grimm **(Utrecht U.) | *Taming Effective Theories*

In this talk I will introduce a generalized notion of finiteness that can provide a structural principle for all effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a Tameness Conjecture that states that valid effective theories are labelled by a definable parameter space and must have scalar field spaces and coupling functions definable using the tame geometry built from a so-called o-minimal structure. The fascinating field of tame geometry has seen much recent progress, which will enable me to support the above swampland conjecture. One piece of evidence arises from a new finiteness theorem for the string theory flux landscape.

###### 26 January 2022, online talk

**Camille Eloy **(VUB) | **AdS3×S3 reductions through exceptional field theory**

I will discuss how to deal with consistent truncations and Kaluza-Klein spectra within exceptional field theory, and demonstrate the efficiency of this framework on the example of AdS3×S3 reductions and deformations thereof. In particular, I will construct a two-parameter family of solutions on squashed spheres, breaking all supersymmetries but yet remaining perturbatively stable.

###### 15 December 2021, Brussels (hybrid format)

**Rodrigo Olea **(Andres Bello U.) | **Conformal renormalization in AdS gravity**

We present evidence that the renormalization of Einstein-AdS gravity can be derived from conformal structures in the bulk. In point of fact, by applying a holographic mechanism which reduces Conformal Gravity to its Einstein sector in 4 and 6 dimensions, the Einstein-AdS action is naturally endowed with the correct counterterms.

**Edoardo Lauria **(Ecole Polytechnique, CPHT) | **Conformal boundary conditions for free fields**

I will discuss the problem of classifying (interacting) conformal boundary conditions for the simplest bulk conformal field theories: free fields. I will mention concrete examples based on perturbation theory, and then describe results using the numerical conformal bootstrap approach, specifically in the case of a scalar field in four and three bulk dimensions.

###### 8 December 2021, online talks

**Alexander Ochirov **(Oxford U.) | *Classical scattering of spinning black holes from quantum amplitudes*

In view of the observations of gravitational-wave signals from black-hole mergers, classical black-hole scattering has received considerable interest due to its relation to the classical bound-state problem of two black holes inspiraling onto each other. In this talk I will discuss the link between classical scattering of spinning black holes and quantum scattering amplitudes for massive spin-s particles. Considering the first post-Minkowskian (PM) order, I will explain how the spin-exponentiated structure of the relevant tree-level amplitude follows from minimal coupling to Einstein’s gravity and in the s → ∞ limit generates the black holes’ complete series of spin-induced multipoles. The resulting scattering function will be shown to encode in a simple way the classical net changes in the black-hole momenta and spins at 1PM order and to all orders in spins. I will then comment on the results and challenges at 2PM order and beyond.

**Gianluca Zoccarato **(Leuven U.) | *S-folds, String Junctions, and 4D N=2 SCFTs*

In this talk I will discuss N=2 SCFTs realised on the worldvolume of D3-branes probing an S-fold plane with 7-branes. I will show how to formulate a projection on string junctions ending on 7-branes that generalises the usual orientifold projection of perturbative string theory to the case of S-fold planes. Using this technique it is possible to read off the flavour symmetry of the SCFT for all possible S-fold planes including the cases with discrete torsion. As a byproduct of this analysis it is possible to understand which representations of the flavour symmetry group are allowed. Finally, I will discuss the computation of central charges of these theories and discuss how to define F-theory in the presence of S-folds with discrete torsion.

###### 1 December 2021, online talks

**Matthias Gaberdiel **(ETH Zurich) | *The string dual of free N=4 SYM*

A proposal for the worldsheet string theory that is dual to free N=4 SYM in 4d is made. It is described by a free field sigma model on the twistor space of AdS5 x S5, and it exhibits a psu(2,2|4)_1 affine symmetry. The theory is a natural generalisation of the corresponding model for tensionless string theory on AdS3 x S3 whose description involves a free field realisation of psu(1,1|2)_1. I will explain how our proposal fits into the general framework of AdS/CFT, and review the various checks that have been performed.

**Marco Fazzi **(U. Milano Bicocca) | **The Cardy-like limit of the superconformal index**

We study the Cardy-like limit of the superconformal index of generic N=1 SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugacities associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. We corroborate the validity of our proposal by studying several examples, beyond the well-understood toric class. We compute the index also for models without a weakly-coupled gravity dual, whose gravitational anomaly is not of order one.

###### 24 November 2021, KUL (hybrid format)

**Davide Cassani **(INFN Padova) | **Effective field theory for the 4d N=1 index on the second sheet**

The counting of BPS states in four-dimensional N=1 theories has attracted a lot of attention in recent years. A generating function (with signs) for this counting problem is the supersymmetric index. This has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates of supersymmetric black holes in AdS_5. The talk will present a manifestly supersymmetric 3d effective field theory approach to the Cardy-like limit on the second sheet. Due to the interaction between massless and massive modes, the 3d theory flows to a trivially gapped vacuum. I will describe how, up to exponentially small corrections, the index is then completely characterized by a universal, finite series made of 3d local terms, the supersymmetric Casimir energy and a very simple logarithmic term.

**Juan Pedraza **(Barcelona U.) | **Riemannian and Lorentzian threads, entanglement and complexity**

I will review recent progress on the reformulation of holographic entanglement entropy in terms of Planck-thickness `bit threads’ and explain the conceptual advantages over the RT prescription. Following the same physical principles, I will then explain how to reformulate the complexity=volume conjecture using `Lorentzian threads’. Conceptually, Lorentzian threads are interpreted as `gatelines’, one-dimensional time-like curves that connect layers of a tensor network grid in the bulk spacetime. Both, in the Riemannian and Lorentzian settings, I will show how Einstein’s equations emerge as a condition on the threads as we impose bulk locality. Based on: 1811.08879, 2007.07907, 2105.08063, 2105.12735, 2106.12585.

###### 17 November 2021, Brussels

**Johannes Lahnsteiner **(U. Groningen) | **Non-Lorentzian Supergravity in Ten Dimensions**

In this talk, I describe recent progress in understanding the background field dynamics of the non-relativistic string theory pioneered by Gomis and Ooguri. Building on earlier developments, I present a non-Lorentzian supergravity theory and explain how it constrains the dynamics of the background fields. Special attention will be given to the exotic geometric structures that arise in this theory. I will compare the results with those coming from beta function calculations. In the final part of my talk, I will comment on non-Lorentzian T-duality and an intriguing relation with double field theory.

**Diego Hofman** (UvA Amsterdam) | **1 dimensional conformal gravity and the Schwarzian theory**

The Schwarzian theory arises as the low energy effective theory of certain quantum mechanical models with random couplings (the SYK model) and some tensor theories. In this talk I will describe another perspective that makes it clear that this is nothing else than conformal gravity in 1-dimension. This perspective elucidates certain technical issues regarding the quantum measure of the theory and allow for an exact calculation of the partition function without invoking localization arguments. I will comment on the significance and applications of this perspective. This is work in progress with D. Anninos and S. Vitouladitis. If there is time I might also discuss the masslessness of the graviton.

###### 10 November 2021, Brussels

**Thomas Mertens **(Ghent U.) | **Liouville and JT quantum gravity**

In this talk, I will discuss recent progress in understanding quantum gravity amplitudes (partition function, boundary correlation functions, and multi-boundary amplitudes) in Liouville gravity, and how they limit to Jackiw-Teitelboim (JT) amplitudes. We focus on two main results: the Liouville gravity answers can be viewed as q-deformations of the JT answers, and Liouville gravity can be written as a 2d dilaton gravity model with a sinh dilaton potential. We end with some prospects towards understanding generic dilaton gravity models.

**Ondrej Hulik** (VUB) | **G-algebroids, a unified framework for exceptional and generalised geometry**

In the talk I will describe the concept of G-algebroid, which generalises both Lie and Courant algebroids, as well as the Leibniz algebroids used in the description of exceptional generalised geometry (at least for n<7). I will discuss a classification results and possible applications of G-algebroids in formulating Poisson-Lie U-duality. The talk is based on a joint work with Mark Bugden, Fridrich Valach and Daniel Waldram.

###### 3 November 2021, online talk

**Shamit Kachru **(Stanford University) | **Fractons and D-branes**

I discuss fractonic field theories, with a focus on the role of foliated field theories and field theories with exotic symmetry in their construction. I then turn to the realization — on systems of branes in string theory — of several novel field theories of this sort.

###### 27 October 2021, online talk

**Miguel Montero **(Harvard University) | **The anomaly that was not meant IIB**

Type IIB supergravity famously has a discrete duality group, which is an exact symmetry of the full type IIB string theory. This symmetry has potential quantum anomalies, which could render the theory inconsistent. In this talk I will describe how we computed these anomalies in recent work, and show they are nonvanishing, but remarkably, they can be cancelled by a subtle modification of the IIB Chern-Simons term in what amounts to a new variant of the Green-Schwarz mechanism. This only happens because of some cancellations that depend on the precise details of the IIB supergravity spectrum. I will also describe alternative ways to cancel this anomaly, presenting variant versions of IIB string theory which have the same IIB supergravity as the low-energy limit, but which differ at the nonperturbative level. These theories may or may not be in the Swampland.

###### 20 October 2021, online talk

**Eric Perlmutter **(IPhT, Saclay) | *On 2D CFT Spectra*

I will explain how the spectra of 2D CFTs, both rational and irrational, exhibit surprising rigidity and determinacy. These structures follow from new ways of leveraging discreteness,

integrality and modularity constraints on torus observables. Our techniques suggest alternative analytic bootstrap approaches to the space of 2D CFTs.

###### 13 October 2021, online talk

**Monica Pate **(NYU) | **Celestial Operator Product Expansions and w_{1+infinity} Symmetry for All Spins**

I will present results pertaining to an investigation into the operator product expansion of massless celestial primary operators of arbitrary spin. I will explain how Poincare symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w_{1+infinity}. Finally, in tree-level minimally-coupled gravitational theories, I will explain how to construct celestial currents from light transforms of conformally soft gravitons that generate the action of w_{1+infinity} on arbitrary massless celestial primaries. The OPEs I will present include those for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

###### 6 October 2021, online talk

**Costis Papageorgakis **(Queen Mary U. of London) | **Towards Solving CFTs with Artificial Intelligence**

I will introduce a novel numerical approach for solving the conformal-bootstrap equations with Reinforcement Learning. I will apply this to the case of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactiﬁed scalar, but the method can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.

###### 29 September 2021, online talk

**Steve Abel **(Durham U.) | *Calculating the Higgs Mass in String Theory*

Almost all existing calculations that concern the Higgs mass are performed within the framework of an effective field theory. While sufficient for certain purposes, such calculations throw up problems to do with fine-tuning and naturalness in particular the famous hierarchy problem. This makes most attempts within field theory to generically understand the Higgs mass pretty much futile. Even most phenomenology done within string theory does not respect the full string symmetries that are responsible for many of the remarkable finiteness properties for which string theory is famous. Chief among these symmetries is worldsheet modular invariance, which is an exact symmetry of all perturturbative closed-string vacua. And yet if the UV is tamed by this symmetry then it should be exact even today! In this talk I will discuss what we can learn from this fact. I describe how a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. I also discuss a number of critical issues involving the use and interpretation of regulators in UV/IR-mixed theories such as string theory. Finally, I show that ultimately the Higgs mass can be understood as arising from an infinity “stringy” sum of Coleman-Weinberg effective potentials in such theories. The results can therefore serve as the launching point for a rigorous investigation of hierarchy problems in a UV complete theory.