Higher level WZW sectors from free fermions

TL;DR

This paper introduces a new method using gauge groups of ambient algebras derived from free fermions to analyze superselection sectors and representation theory in WZW models, exemplified by detailed study of SO(n) at level two.

Contribution

It presents a novel approach employing ambient algebra gauge groups to investigate the structure of WZW theories and their affine Lie algebra representations.

Findings

Established a homomorphism from the gauge group's representation ring to the WZW fusion ring.

Analyzed the SO(n) WZW theories at level two in detail.

Identified the relationship between observable algebra and gauge invariant subalgebra.

Abstract

We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant ambient algebra arises from the description of these conformal field theories in terms of free fermions. As an illustration we analyze in detail the \son\ WZW theories at level two. In this case there is actually a homomorphism from the representation ring of the gauge group to the WZW fusion ring, even though the level-two observable algebra is smaller than the gauge invariant subalgebra of the field algebra.