Week 19.02.2024 – 25.02.2024

In these lectures we will discuss various aspects of conformal field theories in Lorentzian signature. First, we will study the general properties of Lorentzian correlation functions, including their global conformal structure and the relation to Euclidean correlators. We will then consider the Regge limit of correlation functions and how this limit requires the introduction of complex spin. We will define complex spin using the Lorentzian inversion formula, and interpret it in terms of non-local light-ray operators. Finally, we will discuss applications of light-ray operators to even shape observables.

Carroll symmetries were introduced many years ago by Levy-Leblond and Gupta as a possible contraction of the Lorentz symmetries in which effectively the speed of light is sent to zero. The name was inspired by the bizarre property that Carroll particles cannot move. After many years of silence Carroll symmetries have returned to the stage since they have been recognized as symmetries that do occur in several special situations such as the horizon of a black hole. In this presentation I will discuss some of the basic properties and mysteries of Carroll symmetries.

Recently there has been a renewed interest in the subject of novel types of symmetries, now known as generalized symmetries. An interesting question is what happens to these more general symmetry structures upon compactification to lower dimensions. In this talk, we shall explore this in the context of the compactification of 4d N=1 SCFTs to 2d on spheres.

Recent years have seen an upsurge of interest in deformations of two-dimensional sigma-models which preserve classical integrability. Integrability is known to offer powerful techniques for solving such models exactly, even in complex scenarios such as at strong coupling. This talk introduces classical integrability, and the role played by worldsheet dualities in the development of a large family of integrable deformations. The second part of the talk focuses on the application of these deformations within the AdS/CFT correspondence, in order to obtain exact methods for addressing gauge and gravity theories with reduced Noether (super)symmetries. However, current "AdS/CFT integrability" methods are mostly restricted to the undeformed, maximally (super)symmetric instances. To enhance their applicability to a broader range of theoretical models, the concept of “twisted” AdS/CFT integrability is introduced, specifically targeting the “Jordanian” subclass of integrable deformations. Recent and ongoing work in this area will be discussed.