Week 15.01.2023 – 21.01.2023

I will describe a method for approximately solving the crossing equations in a general CFT, using Reinforcement Learning as a stochastic optimiser. I will then present an application of this approach in the context of the 6D (2,0) theory.

We will discuss a connection between OPE algebras appearing in celestial holography for various theories and the `colour-kinematics duality' in the bulk spacetime description of those theories. Both the celestial algebras and the colour-kinematics duality take a particularly simple form for self-dual Yang-Mills and gravity. In particular, we show that the $Lw_{1+\infty}$ celestial algebra recently unveiled in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality. We also present deformations of the celestial algebras resulting from Moyal deformations of the self-dual theories, e.g. the deformation of $Lw_{1+\infty}$ into $LW_{1+\infty}$ in the case of self-dual gravity. In addition, we discuss the relation of these deformations to higher-spin theories of massless particles that can be thought of as extensions of self-dual Yang-Mills and gravity. Finally, we present a proof that tree-level scattering amplitudes in the theories we focus on vanish, signalling their classical integrability, which is an S-matrix version of the Ward conjecture for integrable systems.

In this talk, we will give an overview of the recent developments on the spin chains encoding the spectral problem of four dimensional N=2 superconformal gauge theories.

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.