Carrollian holography suggests that gravity in four-dimensional (4d) asymptotically flat spacetime is dual to a three-dimensional (3d) Carrollian CFT living at null infinity. In this talk, I will review this framework and explain how massless scattering amplitudes in flat space can be recast as Carrollian CFT correlators at null infinity, referred to as Carrollian amplitudes. I will show that these correlators arise naturally from the Carrollian limit of holographic CFT correlators computed via AdS Witten diagrams, establishing a correspondence between the flat-space limit in the bulk and the Carrollian limit at the boundary. As a concrete application, I will briefly discuss the flat-space/Carrollian limit of the duality between 11d supergravity on AdS_4xS^7 and the 3d ABJM theory. Based on arXiv:2312.10138, arXiv:2406.19343 and work in progress.

I will discuss the M2-brane partition function for large class of asymptotically locally AdS_4 x S^7 spacetimes. I will show how supersymmetry localises the M2-brane position to a fixed point of an R-symmetry Killing vector. I will then discuss the one-loop partition function of instantonic M2-branes and show that it is assembled out of building blocks familiar to 3D supersymmetric quantum field theories. I will close out with a discussion of possible one-loop exactness of the answer and what it means for supersymmetric localisation of the M2-brane partition function.

I will provide a rather lengthy introduction in oder to highlight interest in exploring QFts on AdS spaces (without dynamical gravity). The aspects involve the dyanmics of boundaries and interfaces in normal QFTs in flat space, the actual dynamics of confining gauge theories on AdS, the question of prximity in the pace of QFRTs, a more general notion of holography and its connection to S-matrices and finally Euclidean wormholes. All these issues will connect in the effort to describe holographic QFTs on AdS. We shall investigate in a concrete example how the related classical solutions explore the space of QFTs and we construct the general solutions that interpolate between the same or different CFTs with arbitrary couplings. The solution space contains many exotic RG flow solutions that realize unusual asymptotics, as boundaries of different regions in the space of solutions. We find phenomena like "walking" flows and the generation of extra boundaries via "flow fragmentation". We will then move on and describe an example of a holographic theory that confines on flat space, when we put it on AdS. We will find three types of regular solutions are found. Theories with two AdS boundaries provide interfaces between two confining theories. Theories with a single AdS boundary correspond to ground states of a single confining theory on AdS. We find solutions without a boundary, whose interpretation is probably as interfaces between topological theories. We analyze in detail the holographic dictionary for the one-boundary solutions and compute the free energy. No (quantum) phase transitions are found when we change the curvature. We find an infinite number of pure vev solutions, but no CFT solution without a vev. We also compute the free energy of the interface solutions. We find that the product saddle points have always lower free energy than the connected solutions. Finally we will comment on the spectrum of propa gating states of holographic theories on AdS and dS.

We extend the powerful property of Yangian invariance to a new large class of conformally invariant multi-loop Feynman integrals. This leads to new highly constraining differential equations for them, making integrability visible at the level of individual Feynman graphs. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. The graphs we consider determine correlators in the recently proposed "loom" fishnet CFTs. The construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs. We also relate these equations in certain cases to famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators, opening the way to using new powerful solution methods.

About fifty years ago, Gibbons and Hawking argued that the Euclidean gravitational path integral with suitable boundary conditions can be interpreted as a grand-canonical partition function. Classical gravitational solutions, including black holes, arise as saddles of this path integral, and from the saddle-point action one can extract the black hole entropy. In the talk, I will discuss some recent developments of these ideas. Working in five dimensions, we will see how imposing supersymmetric boundary conditions converts the partition function into an index. Then we will construct a class of saddles of this index which interpolates between supersymmetric black holes and horizonless microstate geometries. I will discuss how the saddle point action can be computed via equivariant localization. Finally, I will comment on the relevance of these findings for black hole microstate counting and holography.

I explore decoupling limits that lead to matrix theories on D-branes, focusing on their BPS nature and the emergence of non-Lorentzian target space geometries. In these limits, D-branes experience instantaneous gravitational forces, and when applied to curved geometries, it is shown that a single decoupling limit leads to the AdS/CFT correspondence. By applying two such limits, we generate new holographic examples, including those with non-Lorentzian bulk geometries. I also discuss the relationship between matrix theories and non-relativistic string theory, and their uplift to M-theory. Finally, we demonstrate that reversing these decoupling limits connects to the TTbar deformation in two dimensions. This provides a new perspective on the near-horizon brane geometry and leads to TTbar-like flow equations for the Dp-brane DBI action.

The oldest and best established Swampland constraint is perhaps the idea that there are no global symmetries in quantum gravity. Traditionally, this idea has been regarded as not strong enough to strong constraints at low energies, since the quantum gravity symmetry breaking effects could be extremely weak. I will describe recent progress in Swampland, in conjunction with developments in generalized and non-invertible symmetries, which have led to the discovery of new branes in string theory, new mechanisms to engineer small couplings in string theory, and even ruling out some effective field theories in higher dimensions.

I will briefly review the classical double copy, which maps exact solutions of classical gauge theories like electromagnetism, to solutions of general relativity. We will discuss why a position-space map is feasible, and then relate several gravitational objects (including horizons, Penrose limits, and asymptotics) to their gauge theory analogues.

I will explain how the recent developments in so-called categorical or non-invertible symmetries can be used to make sharp predictions about phases -- gapped and gapless -- in the presence of such symmetries. This so-called a categorical Landau paradigm applied to 1+1d systems predicts new phases and phase transitions. In some instances these are extremely simple to implement in spin-chains and have a potential to be implemented in the very near future in cold atom systems

The study of non-abelian gauge theories in compact or non-flat spaces can be useful to gather insights and new perspectives on the confinement problem. We consider Yang-Mills theory on four dimensional Anti-de Sitter space and wonder how signals of confinement in the bulk can be detected from boundary observables. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space and hence a deconfinement-confinement transition has to occur as the radius is increased. By perturbative computations we provide evidence for the scenario of merger and annihilation. Namely, the theory with Dirichlet boundary condition stops existing because it merges and annihilates with another theory. We also derive a general result for the leading-order anomalous dimension of the so called displacement operator for a generic perturbation in Anti-de Sitter, showing that it is related to the beta function of bulk couplings.

15:00 - Jeremy Mann: "Semiclassical N-body Problem in AdS at Large Spin" // 15:20 - Azadeh Maleknejad: "Stochastic Fermion Creation: Remnant of Gravitational Chiral Anomaly" // 15:40 - Refreshments // 16:10 - Ofer Lahav (UCL): "The Status of Dark Energy Observations" // 17:00 - Pub

The perturbative expansion of quantum field theory expresses physical quantities as series of numbers (or functions) associated to combinatorial graphs, called Feynman integrals. These integrals are hard to compute, and furthermore their sum forms a series that is in fact divergent. To gain insights into the large order behaviour, Feynman integrals can be approximated astonishingly well by easily computable combinatorial invariants of graphs. I will discuss two such approximations: the tropical Feynman integral and the Martin invariants, using phi^4 theory as an example. The Martin invariants are related to the O(-2) symmetric vector model and can be generalized to an integer sequence. I will end explaining how this sequence encodes the exact value of a Feynman integral through a limit used by Apery to prove the irrationality of zeta(3).

Entanglement entropy in quantum field theory is UV-divergent, which makes it a challenging quantity to analyze from an algebraic perspective. In this talk, I will describe how perturbatively coupling to gravity improves this situation, resulting in a well-defined notion of renormalized entropy in the semiclassical limit. This entropy is constructed using techniques from the theory of von Neumann algebras, and agrees with the generalized entropy of a subregion, consisting of the sum of the quantum field entanglement entropy and the area of the entangling surface. As an application, I will show how to derive the generalized second law for black hole horizons in terms of this renormalized entropy. Time permitting, I will also discuss a construction of a gravitational von Neumann algebra in a slow-roll inflation background, and describe how the background provides an intrinsic notion of a cosmological observer.

I will revisit the problem of defining an invariant notion of brane tension, analogous to the ADM mass, in a theory of gravity. I will propose two natural definitions, a gravitational and an inertial tension, in terms of asymptotic data akin to that of a Defect CFT. I will illustrate these definitions with various examples, and present the evidence why for supersymmetric branes the two tensions must be equal.

Flat space admits a foliation by AdS leaves. One seeks to derive the bulk to boundary dictionary for flat space holography as the uplift of the AdS/CFT dictionary.Over the last year progress on this front has been made by isolating the contribution to bulk amplitudes associated to a single AdS leaf. This has culminated in the construction of a 2D leaf CFT, consisting of a Liouville field, a level one current algebra and a weight -3/2 fermion, which reproduces the bulk tree MHV gluon amplitude. This talk will review these developments.

The numerical S-matrix Bootstrap aims at establishing non-perturbative universal bounds on physical observables that can be extracted from scattering amplitudes in any dimension. In the first part of the talk, I will review our past explorations of the space of supergravity amplitudes and their connection to String/M theory. I will discuss the universal bounds on the first non-universal correction to sugra amplitudes, and how the extremal solution is compatible with clustering in the Born regime, and with the Quantum Regge growth hypothesis. In the second part of the talk I will report on a first Bootstrap exploration of multi-particle scattering. I will focus on the simplest non-integrable S-matrix describing the scattering of branons on the world-sheet of confining strings in three dimensions.