Examples of subfactors from conformal field theory

TL;DR

This paper explores the connection between subfactors and conformal field theory (CFT), identifying specific subfactors from known CFT and constructing new ones from holomorphic CFT with central charge 24.

Contribution

It identifies a particular subfactor with an intermediate subfactor from conformal inclusion and constructs new subfactors from recent holomorphic CFT research.

Findings

Identified the $3^{ ext{Z}_2 imes ext{Z}_2}$ subfactor with an intermediate subfactor from conformal inclusion.

Constructed new subfactors from holomorphic CFT with central charge 24.

Provided evidence supporting the conjecture that all finite depth subfactors relate to CFT.

Abstract

Conformal field theory (CFT) in two dimensions provide a rich source of subfactors. The fact that there are so many subfactors coming from CFT have led people to conjecture that perhaps all finite depth subfactors are related to CFT. In this paper we examine classes of subfactors from known CFT. In particular we identify the so called $3^{\Z_2\times \Z_2}$ subfactor with an intermediate subfactor from conformal inclusion, and construct new subfactors from recent work on holomorphic CFT with central charge $24$.