CFT fusion rules, DHR gauge groups, and CAR algebras

TL;DR

This paper shows that certain conformal field theories with braid group statistics can be described using DHR gauge groups, connecting various models like orbifolds, WZW theories, and free fermions.

Contribution

It demonstrates the applicability of DHR theory to a broader class of conformal field theories, including orbifolds and WZW models, clarifying their superselection structures.

Findings

CFTs with braid group statistics can be described via DHR gauge groups.

Includes analysis of c=1 orbifold and level two so(N) WZW theories.

Establishes links between these models and free fermion theories.

Abstract

It is demonstrated that several series of conformal field theories, while satisfying braid group statistics, can still be described in the conventional setting of the DHR theory, i.e. their superselection structure can be understood in terms of a compact DHR gauge group. Besides theories with only simple sectors, these include (the untwisted part of) c=1 orbifold theories and level two so(N) WZW theories. We also analyze the relation between these models and theories of complex free fermions.