Arbeitsgemeinschaft: Conformal Field Theory

Abstract

The two major approaches to chiral conformal field theory – one based on operator algebras and one based on vertex algebras – both lead to representation categories which are tensor categories and, in the case of rational chiral conformal field theories, more specifically modular tensor categories. In this Arbeitsgemeinschaft, we have studied algebraic structures related to tensor categories arising in conformal field theory. The notion of a module category over this tensor category is central in the construction of a full local conformal field theory in various frameworks.