Conformal Field Theory, Vertex Operator Algebras and Operator Algebras

TL;DR

This paper reviews recent advances in local conformal nets, highlighting their connections to vertex operator algebras and operator algebras in the context of chiral conformal field theory.

Contribution

It elucidates the relationship between operator algebraic approaches and vertex operator algebra formulations of chiral conformal field theory.

Findings

Progress in understanding local conformal nets

Connections established between operator algebras and vertex operator algebras

Representation theoretic insights into chiral conformal field theory

Abstract

We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras which gives a different and algebraic formulation of chiral conformal field theory.