Conformal nets are factorization algebras

TL;DR

This paper demonstrates that conformal nets of finite index can be viewed as factorization algebras, linking algebraic structures in conformal field theory to broader mathematical frameworks.

Contribution

It establishes that conformal nets of finite index are a specific example of factorization algebras, advancing the understanding of their algebraic and categorical properties.

Findings

Conformal nets of finite index are factorization algebras.

The result aids in proving equivalences between categories of positive energy representations.

Supports the connection between conformal nets and factorization algebra frameworks.

Abstract

We prove that conformal nets of finite index are an instance of the notion of a factorization algebra. This result is an ingredient in our proof that, for $G=SU(n)$, the Drinfel'd center of the category of positive energy representations of the based loop group is equivalent to the category of positive energy representations of the free loop group.