Fusion of two conformal defects in conformal field theory can be understood as an RG flow whose IR fixed point is another conformal defect, with the running scale is set by the separation between the defects. When the separation is small, the system can be described by EFT techniques, in terms of an effective action on the IR defect. In this talk I will discuss the constraints that conformal symmetry imposes on such effective actions, and the implications of this picture for observables such as the cusp anomalous dimension. Joint work with Alexander Radcliffe and Ritam Sinha, arXiv:2406.04561.

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.

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.

Abstract: On general grounds, the spectrum of a Conformal Field Theory (CFT) is expected to be extremely complicated away from special limits. One of such limits consists of the lowest energy states for every given spin, which are also known as the leading-twist states. In this talk I will discuss the structures that emerge in the spectrum as one departs from this limit towards the higher-twist states, focusing especially on the Regge trajectories. In particular, I will describe a general mechanism that reconciles the idea of Regge trajectories with the growing number of local operators at large spin. I will then demonstrate how this mechanism works in the case of one-loop phi^4 Wilson-Fisher theory in epsilon-expansion. This example will also clarify the properties of double-twist trajectories and light-cone bootstrap at higher-twist. Finally, I will briefly discuss a work in progress on going beyond the double-twist limit.

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.

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.