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 cat- egories. 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.
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