The Relation between Subfactors arising from Conformal Nets and the Realization of Quantum Doubles

TL;DR

This paper establishes a connection between subfactors from conformal nets and their realization via quantum doubles, providing a new framework for understanding their classification and structure.

Contribution

It defines conditions under which a subfactor arises from a conformal net, linking it to the quantum double of the subfactor's representation category.

Findings

Subfactors can be characterized by their relation to conformal nets.

The representation category of a conformal net can be the quantum double of a subfactor.

A precise criterion for when a subfactor arises from a conformal net is provided.

Abstract

We give a precise definition for when a subfactor arises from a conformal net which can be motivated by classification of defects. We show that a subfactor $N \subset M$ arises from a conformal net if there is a conformal net whose representation category is the quantum double of $N\subset M$.