Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles

TL;DR

This paper develops a field theory framework for Dijkgraaf-Witten models with abelian gauge groups that exhibit non-abelian topological order, analyzing their spectra, correlation functions, and fusion rules.

Contribution

It provides a comprehensive field theoretic analysis of DW models with abelian gauge groups and non-abelian quasiparticles, including spectra, correlation functions, and fusion rules.

Findings

Non-abelian statistics appear in DW theories with abelian gauge groups.

Calculated correlation functions and fusion rules for line operators.

Filled a gap in the literature on the spectra of these models.

Abstract

Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting -- the goal of this work is to fill the gap in the literature, at least for a selection of DW models with abelian gauge groups but non-abelian topological order. As applications, various correlation functions and fusion rules of line operators are calculated. We discuss for example the appearance of non-abelian statistics in DW theories with abelian gauge groups.