Generalised notions of symmetries have received widespread attention in recent years. Though exotic, such generalised symmetries have been shown to naturally arise for instance as dual symmetries upon gauging ordinary symmetries. In this talk, I will present a systematic framework to investigate dualities of quantum lattice models and study the resulting generalised symmetries. I will illustrate this framework in the context of familiar spin models.

When computing scattering amplitudes in dimensional regularization, one frequently encounters contributions whose integrands vanish in strictly four dimensions. While these "evanescent" integrals can be handled with dimensional shift identities at one-loop, a similar treatment at the next perturbative order is insufficient. In this talk, we introduce a novel systematic method to compute evanescent contributions. By employing the local subtraction method of Anastasiou and Sterman we show that evanescent Feynman integrals are controlled by regions of loop-momentum space associated to ultra-violet, soft or collinear divergences. These integrals are then reduced to either products of one-loop integrals or one-fold integrals thereof. Starting from known integrands, we use this technique to easily recompute the leading-color two-loop four- and five-gluon QCD amplitudes in the all-plus helicity configuration. Remarkably, we find that the finite remainder is given by contributions arising from only ultra-violet regions of momentum space, and that the collinear contributions cancel in a highly non-trivial way.

We will overview some of the recent progress regarding IR dualities across dimensions. In such dualities one engineers the same low energy QFT starting from high energy descriptions in different space-time dimensions. We will review how various strong coupling phenomena can follow from embedding the system of interest in such an across dimensions setup. We will also outline some of the open problems/questions in the field.

In this talk I will discuss aspects of global symmetry and their t Hooft anomalies in lattice systems. I will discuss how anomalies are defined and probed using topological defects, which will be applied to both internal and lattice symmetries. The latter arise in systems satisfying Lieb-Schultz-Mattis-type theorems. Using the example of a spin-1/2 XXZ chain, I will also discuss how the continuum limit of a lattice model is properly described in terms of a low-energy theory with topological defects. In particular, I will show that t Hooft anomaly explains a curious size dependence of the ground state lattice momentum in the spin-1/2 XXZ chain.

We propose a (bosonic) worldsheet description of two-dimensional Yang-Mills. We also argue that similar worldsheet actions provide candidate duals to the symmetric product orbifolds for arbitrary seed CFTs.

In this talk I will discuss how to compute amplitudes on AdS, using the analytic conformal bootstrap and the AdS/CFT correspondence. I will also discuss how to include higher trace operators in a simplified setup.

In this talk we will explore a class of 3d N=2 theories labeled by graphs and related to quivers in an unusual way. Unlike quiver gauge theories --- a class of Lagrangian field theories widely used in modern QFT --- theories that we consider are non-Lagrangian, in a sense that they can be defined as IR fixed points of gauge fields coupled to non-linear matter as in the Skyrme models of nuclei. Just like the physics of the Skyrme model is intimately tied to symmetries of QCD, generalized symmetries play an important role in these 3d N=2 theories. The connection to quivers, on the other hand, arises in a way that is not standard in modern particle physics, but is standard in the study of logarithmic CFTs and motivic DT invariants. Download Mathematica demonstration here: theory.caltech.edu/~gukov/Plumbed.nb 3d Modularity software: https://github.com/d-passaro/pySeifert

Abstract: I will present a way to promote the anomalous axial U(1) in 4d QED to an exact symmetry, with the price of losing its invertibility. I will then discuss some applications of this non-invertible U(1) symmetry. In particular, I will show how to couple this non-invertible symmetry to a gauge field. By taking this gauge field to be dynamical, we get a new type of gauge theory with unconventional interactions and constraints. By taking this gauge field to be background, we can study 't-Hooft anomalies of the non-invertible symmetry.

In this talk I will give you an update of the status of the classification of superconformal field theories in four dimensions. After reviewing the basic properties which make the classification of theories with both supersymmetry and conformal invariance possible, I will describe in detail the framework which allows for a bottom up analysis and summarise the latest results in rank-2.

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.