Higher symmetry and gapped phases of gauge theories

TL;DR

This paper explores topological field theories for gapped phases of gauge theories with higher symmetry, classifying their actions and observables, and proposing new matter phases protected by these symmetries.

Contribution

It generalizes Dijkgraaf-Witten theory using 2-groups and classifies topological actions and observables for these higher symmetry gauge theories.

Findings

Classified topological actions for higher symmetry gauge theories

Established duality relations with Dijkgraaf-Witten theory

Proposed new phases of matter protected by higher symmetry

Abstract

We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf-Witten theory by replacing a finite group by a finite 2-group. The basic field in this TQFT is a 2-connection on a principal 2-bundle. We classify topological actions for such theories as well as loop and surface observables. When the topological action is trivial, the TQFT is related to a Dijkgraaf-Witten theory by electric-magnetic duality, but in general it is distinct. We propose the existence of new phases of matter protected by higher symmetry.