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

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 $N\subset M$.

10 pages