Conformal Field Theory, Tensor Categories and Operator Algebras

TL;DR

This paper provides lecture notes on the operator algebraic approach to 2D conformal field theory, emphasizing representation theory and connections to vertex operator algebras, suitable for newcomers without prior background.

Contribution

It offers an accessible introduction to the operator algebraic framework for conformal field theory, linking it to vertex operator algebras and representation theory.

Findings

Clarifies the operator algebraic structure of 2D conformal field theories

Highlights connections between operator algebras and vertex operator algebras

Provides foundational knowledge for further research in mathematical physics

Abstract

This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or quantum field theory is assumed.