Quantum symmetries in discrete gauge theories

TL;DR

This paper investigates the properties of non-abelian anyons in (2+1)-dimensional discrete gauge theories, revealing how the gauge symmetry extends to a Hopf algebra structure at the quantum level.

Contribution

It provides a detailed analysis of the fusion, braiding, and scattering of non-abelian anyons, and shows the extension of the gauge symmetry to a Hopf algebra D(H) in quantum theory.

Findings

Identification of quantum numbers for charged sectors

Extension of symmetry group to Hopf algebra D(H)

Relevance to (3+1)-dimensional theories

Abstract

We analyse the fusion, braiding and scattering properties of discrete non-abelian anyons. These occur in (2+1)-dimensional theories where a gauge group G is spontaneously broken down to some discrete subgroup H. We identify the quantumnumbers of the electrically and magnetically charged sectors of the remaining discrete gauge theory, and show that on the quantum level the symmetry group H is extended to the (quasi-triangular) Hopf algebra D(H). Most of our considerations are relevant for discrete gauge theories in (3+1)-dimensional space time as well.