We discuss numerical results from integrability for the Hagedorn temperature in N=4 SYM and ABJM theory at strong coupling and compare them to the Hagedorn temperatures of their string theory duals. From the numerics we conjecture the leading analytic coefficients in the expansion about large 't Hooft coupling. This talk is based on arXiv:2306.09883 and arXiv:2307.02350.

I will discuss recent and ongoing work with Emil Have, Stefan Prohazka and Jakob Salzer on possible kinematics for flat space holography. I will discuss how a seemingly novel projective compactification of Minkowski spacetime reveals a rich asymptotic geometry homogeneous under the Poincare group and including the blow-ups at spatial and timelike infinities as well as a novel four-dimensional space intimately associated to null infinity. This allows for novel geometric descriptions of the Minkowski asymptotic geometries and gives us a glimpse of the asymptotic geometry of asymptotically flat spaces.

The standard formulation of General Relativity is based on a geometrical framework where the spacetime manifold is endowed with a Lorentzian metric and its associated Levi-Civita connection. Since the affine structure is independent of the metric, it is possible to extend this geometrical set-up to allow for more general connections, thus giving rise to the metric-affine framework where the new actors are the torsion and the non-metricity. After discussing how these two objects can provide equivalent descriptions of GR, I will discuss how pathologies arise in modified theories of gravity along different directions in the metric-affine landscape. [please email a.held@imperial.ac.uk for zoom link or password]

I review the emergence of JT gravity from the SYK model, and the calculation of correlation functions in JT gravity. I motivate the need for a new observable distinct from entanglement entropy to fully decode emergent gravity, and propose as such an observable a quantum generalization of the entropy of multiple measurements on a dynamical system. Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting.

I will introduce the framework of 4D scattering equations for calculating tree level super amplitudes in a variety of different theories, including Einstein supergravity and super Yang-Mills theory. I will discuss my work on numerical solutions to these equations by Monte Carlo methods, and work with Arthur Lipstein on calculating N=4 conformal supergravity amplitudes in this framework.

I will report on joint work with Andrea Santi outlining an algebraic reformulation of the classification problem of eleven-dimensional supergravity backgrounds. The basic object of study is the Killing superalgebra of the background, whose algebraic structure has recently been elucidated. If time permits I will also comment on work also involving Paul de Medeiros applying these techniques to the construction of rigidly supersymmetric theories in curved spaces.

One can easily be frustrated by the tremendous redundancy in possible physical description. By this I mean the freedom to choose gauge, make field redefinitions, add any amount of auxiliary spectator matter, and the such. Happily we can exploit such freedom to encourage the emergence of a new duality in gauge theories. The existence of a duality between color and kinematics exposes a hidden local double-copy structure inherent to prediction in many theories. This structure weaves its way between theories both formal and phenomenological, from QCD to Gravity, from Chiral Perturbation Theory to Born-Infeld and Volkov-Akulov, and from open to closed superstring theories. The duality is sharpest at the level of the perturbative S-matrix — so I will focus my talk there, although I will also mention some recent provocative work beyond scattering. I will mainly discuss progress and challenges to generically achieving color-dual kinematic representations at the multi-loop level. I present a path forward that introduces, at least temporarily, a redundancy of description that we can exploit to map a set of functional relations to linear ones. I will talk about this approach in terms of a geometric picture involving the graph of local graphs, discussing tradeoffs and applicability to long-standing problems.

We study the general formulation of gauged supergravity in seven dimensions with sixteen supercharges keeping duality covariance by means of the embedding tensor formalism. We first classify all inequivalent duality orbits of consistent deformations. Secondly, we analyse the complete set of critical points in a systematic way. Interestingly, we find the first examples of stable de Sitter solutions within a theory with such a large amount of supersymmetry.

A review will be provided on the renormalization program for the so-called Tensor Models for Quantum Gravity. These are non local field theories extending both the matrix models, a successful framework in statistical mechanics applied to 2D physics, and the Grosse-Wulkenhaar model in the matrix basis arising in Noncommuting Neometry. We will emphasize the Multi-scale renormalization but also report recent results on the Functional Renormalization Group Approach for these class of models.

Certain classes of supersymmetric Yang-Mills (SYM) theories including the well known N=4 SYM, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. In this talk I will provide the constructions of such theories and describe how great ideas such as topological field theories, Dirac-Kahler fermions, geometric discretization all come together to create lattice SYM theories that are exact-supersymmetric, gauge-invariant, local and doubler-free on the lattice. Then I move on to discuss the recent lattice constructions of specific classes SYM theories in two dimensions, with matter in various representations.

Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature gravity. It admits a family of AdS vacua, most (but not all) of them supporting black holes, that display interesting features such as a generalized variant of the Hawking-Page phase transition. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT correspondence which I will discuss in this talk.

TransPlanckian inflationary excursions are very interesting because they are sensitive to Planck-suppressed operators and can generate observable tensor modes. I review one proposed model generating a transPlanckian excursion and argue that consideration of antibrane backreaction renders the assumptions entering the model inconsistent.

We've known since childhood that symmetry can be a very powerful tool in solving partial differential equations. With a little symmetry, one can reduce the number of independent variables, whereas with some more symmetry one can usually separate variables and reduce the problem to solving ordinary differential equations. Given enough symmetry, though, partial differential equations become algebraic. A large body of current research in our field requires finding solutions to the (super)gravity field equations and in this talk I will motivate the search for homogeneous supergravity backgrounds and mention some recent results in this area.

Local string models are those where Standard Model degrees of freedom arise on a small region inside a large bulk volume. I study threshold effects on gauge coupling running for such models. The Kaplunovsky-Louis formula for locally supersymmetric gauge theories predicts the unification scale should be the bulk winding mode scale, parametrically large than the string scale where divergences are naively cut off. Analysis of explicit string models on orbifold/orientifold geometries confirms this. The winding mode scale arises from the presence of tadpoles uncancelled in the local model. I briefly discuss phenomenological applications to supersymmetry breaking and gauge coupling unification.

I will discuss several constructions of superalgebras associated to the Killing spinors of a supergravity background, with special emphasis on the ten- and eleven-dimensional supergravities.

I'll introduce a combinatorial problem on tilings of the plane by rhombi and explain how the solution is related to the representation theory of groups.

I review general features of AdS/CFT models with dynamical quarks, with particular emphasis on chiral dynamics. I also show how these models incorporate the nontrivial interplay between the solution of the U(1) problem in QCD and the 1/N expansion.