Operator algebras and vertex operator algebras

TL;DR

This paper explores the connection between vertex operator algebras and conformal nets in two-dimensional conformal field theory, providing a new construction method linking algebraic and analytical frameworks.

Contribution

It presents the first general construction of conformal nets derived from unitary vertex operator algebras, bridging two mathematical formulations of chiral CFT.

Findings

Established a method to construct conformal nets from VOAs

Unified algebraic and analytical approaches in chiral CFT

Provided new insights into the structure of two-dimensional CFTs

Abstract

In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are two mathematical formulations of chiral CFT, the one based on vertex operator algebras (VOAs) and the one based on conformal nets. We describe some recent results which, for first time, gives a general construction of conformal nets from (unitary) VOAs.