Quasiparticle operators with non-Abelian braiding statistics

TL;DR

This paper investigates gauge invariant fermions in $SU(N)_k$ Wess-Zumino-Witten models, revealing their role in creating physical quasiparticles with non-Abelian braiding, and providing a holomorphic factorization of primaries.

Contribution

It introduces explicit gauge invariant fermions that realize non-Abelian braiding and holomorphic factorization in $SU(N)_k$ Wess-Zumino-Witten models.

Findings

Fermions create physical quasiparticles with non-Abelian braiding.

Explicit holomorphic factorization of primaries achieved.

Provides a new framework for understanding non-Abelian anyons.

Abstract

We study the gauge invariant fermions in the fermion coset representation of $SU(N)_k$ Wess-Zumino-Witten models which create, by construction, the physical excitations (quasiparticles) of the theory. We show that they provide an explicit holomorphic factorization of $SU(N)_k$ Wess-Zumino-Witten primaries and satisfy non-Abelian braiding relations.