The structure of the gauge group constrains the properties of operators in a G-gauge theory. In this talk, I will consider the reverse direction and ask what properties of a (finite) gauge group can be reconstructed from the operators. I will first consider OPE/fusion rules of Wilson lines and explain various properties of the gauge group that can be reconstructed from it. Then I will introduce certain surface operators which exist in any G-gauge theory. I will describe the fusion rules of these surface operators and show that, in general, there are properties of the gauge group that can be deduced from the fusion rules of surface operators which cannot be obtained from the fusion rules of Wilson lines, and vice-versa.

A key difference between black holes and ordinary thermal systems is the absence of a pressure-volume work term in the first law of black hole thermodynamics. It is possible to introduce such a work term for black holes in backgrounds with a cosmological constant by treating the cosmological constant as a pressure, offering a rich gravitational perspective on everyday phenomena. Missing, however, is justification for allowing variations of the cosmological constant. In this talk I will present a higher-dimensional origin of 'extended black hole thermodynamics' using holographic braneworlds. In this set-up, gravity is coupled to a lower-dimensional brane such that classical black holes in a bulk anti-de Sitter spacetime correspond to exact quantum corrected black holes localized on the brane, including all orders of semi-classical backreaction. Crucially, varying the tension of the brane leads to a dynamical cosmological constant on the brane, and, correspondingly, a variable pressure attributed to the brane black hole. In other words, standard thermodynamics of classical black holes induces extended thermodynamics of `quantum' black holes on a brane. As proof of concept, I will present the extended thermodynamics of the quantum BTZ black hole, also providing a microscopic interpretation using `double holography’.

Local Schur operators in 4d N=2 SCFTs form a protected class of operators giving rise to a 2d vertex operator algebra. Following the local operator picture, we introduce classes of conformal extended operators (lines, surfaces) and study these in twisted Schur cohomology. We show how these operators support a vertex algebra structure, extending the VOA picture of local Schur operators.

I will explain how, in boundary conformal field theories, global symmetries broken by boundary conditions generate a homogeneous conformal manifold. These manifolds are cosets, and I will give fully two worked out examples in the case of free fields of spin zero and one-half. These results give simple illustrations of the salient features of conformal manifolds, which I will review, while generalising to interacting setups.

In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will review this connection for scattering amplitudes. After a broad review of the main ingredients involved, I will focus on maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory -- the momentum amplituhedron. In particular, I will show how such geometry encodes the properties of amplitudes. Finally, I will discuss some of the questions which remain open in this framework.

Quantum field theory of higher-spin particles is a formidable subject, where preserving the physical number of degrees of freedom in the Lorentz-invariant way requires a host of auxiliary fields. They can be chosen to have a rich gauge-symmetry structure, but introducing consistent interactions in such approaches is still a non-trivial task, with massive higher-spin Lagrangians specified only up to three points. In this talk, I will discuss a new, chiral description for massive higher-spin particles, which in four spacetime dimensions allows to do away with the unphysical degrees of freedom. This greatly facilitates the introduction of consistent interactions. I will concentrate on three theories, in which higher-spin matter is coupled to electrodynamics, non-Abelian gauge theory or gravity. These theories are currently the only examples of consistently interacting field theories with massive higher-spin fields.

The eikonal exponentiation provides a way to obtain the classical limit of gravity amplitudes and to calculate the total deflection in collisions of compact objects in the Post-Minkowskian (PM) regime. In this talk I will illustrate how the eikonal phase can be promoted to an operator combining elastic and inelastic amplitudes in order to account for gravitational-wave emissions. Up to 3PM order, this restores manifest unitarity and allows us to calculate the linear and angular momentum of the gravitational field after the collision, as well as the changes in the linear and angular momenta of the colliding bodies. In this way, one can explicitly check the corresponding balance laws. I will also explain how the framework easily accommodates both radiative effects, static effects, and linear tidal corrections.

W-algebras are ubiquitous extended symmetries of a vast class of CFTs, with deep connections to quantum groups and integrability. Recently, through the techniques of celestial holography, the W_{1+inf} algebra was realized explicitly in celestial correlation functions associated to 4d gravitational scattering amplitudes, but the connection to other realizations of the symmetry, and in particular integrability, was vaguely understood. In this talk I will attempt to shed some light on this issue, arguing that the emergence of the symmetry is directly connected to the color-kinematics duality relating gravity and gauge theory amplitudes, at the same time unveiling an associative structure in collinear singularities of the tree-level S-Matrix.

In this talk, I shall consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories. I shall give a general BRST and anti-BRST invariant formulation of linearised $\mathcal{N}=0$ supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. I shall then demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.

Results in Quantum Field Theories, such as anomalous dimensions or scattering amplitudes are known to exhibit rich properities under the Galois coaction that acts on period integrals. I will show how these phenomena arise directly from an integrability setup describing certain anomalous dimensions of an integrable four-dimensional scalar model. I will also discuss a conjectural all-loop differential equation for these quantities, constructed from derivatives with respect to Riemann zeta values.

I will present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we obtain the OPE data of heavy-light double-twist operators directly from instanton counting in the SU(2) gauge theory.

One way of probing quantum entanglement is to identify a multi-player task (a “game”) that can be won more reliably when the players share a specific entangled quantum state. I will review some well-known quantum games, and discuss how these can be generalized to games which exploit the entanglement structure of a phase of matter rather than a specific quantum state.

Quantum annealers are near-term adiabatic quantum computing devices that are already of significant size. In this talk I discuss how they can be used as laboratories to implement genuine tunnelling in Quantum Field Theories. I also discuss how they can be used to embed and train a general neural network in a quantum annealer without introducing any classical element in training. This approach opens a novel avenue for the quantum training of general machine learning models which can incorporate virtually limitless and changing training data. The talk will include a pedagogical introduction to quantum annealing.

I will discuss recent developments in the characterisation of asymptotic states in asymptotically flat gravity, and the central role played by BMS fluxes in connection to soft graviton theorems. As a result of these new ideas, I will show that the subleading soft graviton theorem including loop effects is the Ward identity associated with superrotations symmetries. We will conclude that BMS symmetries are genuine symmetries of the gravitational S-matrix beyond the classical regime.

Whereas scattering amplitudes probe physics at the shortest distances, cosmology probes physics at the largest scales. Nevertheless, many concepts discovered in the study of scattering amplitudes have an analogue for cosmological observables. In this talk I will describe some aspects of this program which I have recently been investigating such as the double copy, scattering equations, and soft limits, and will discuss how these directions are interrelated.

As part of the SAGEX Closing Meeting being held at Queen Mary's University of London in June 2022, we are delighted that world-renowned theoretical physicist, Professor Nima Arkani-Hamed will deliver the meeting's colloquium. We welcome undergraduate and postgraduate students, and researchers and academics to attend this exciting event. Please register at: https://www.eventbrite.co.uk/e/sagex-colloquium-nima-arkani-hamed-tickets-256058035477

The moduli space of Supersymmetric gauge theories with 8 supercharges has a rich structure of symplectic singularities associated with degenerations in which additional massless states arise. These are neatly arranged into phase diagrams that encode the different sets of massless states, with information on the moduli that are needed to be tuned in order to move from one phase to another. We will present results from studies of families of quivers, including those on the affine grassmanian of finite dimensional Lie algebras. ; part of the London TQFT Journal Club (please register at https://london-tqft.vercel.app)

For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. We give an explicit realization of this duality defect in the free Maxwell theory. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

There exist low-dimensional models of holography in which the bulk gravitational theory is dual to an ensemble average of boundary quantum field theories (as opposed to a single theory). In the case of three-dimensional gravitational theories based on topological field theories, we draw a connection between the ensemble averaging (and the lack of factorization of the partition function) and the presence of global symmetries. Once the global symmetries are removed (by a suitable gauging procedure), the gravitational theory behaves as a unitary quantum system.; Part of London TQFT Journal Club; please register at https://www.london-tqft.co.uk;

In this talk I will present an overview of the local holography program which links the quantization of gravity with the representation theory of infinite dimensional symmetry groups attached to codimension 2 surfaces: the corners. I will present in detail the corner symmetry group for 4d gravity and show its connection with the symmetry algebra of perfect fluids. As a step towards quantization, I will recall the importance of the co-adjoint orbit method and I will derive a complete classification of the positive-area coadjoint orbits of this group for corners that are a 2-sphere. I will also show that a deformation of this symmetry group naturally involves matrix model as a quantum regulator. If time permits I will mention some connections these results have with celestial holography and the higher spin asymptotic symmetry group. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]