Higher abelian Dijkgraaf-Witten theory

TL;DR

This paper generalizes Dijkgraaf-Witten theories to include higher-form gauge fields valued in finite abelian groups, extending the framework to codimension 2 in quantum field theory.

Contribution

It introduces a higher abelian Dijkgraaf-Witten theory based on p-form gauge fields, expanding the scope of topological quantum field theories.

Findings

Defines higher abelian Dijkgraaf-Witten theories

Extends the framework to codimension 2

Provides a mathematical formulation for p-form gauge fields

Abstract

Dijkgraaf-Witten theories are quantum field theories based on (form degree 1) gauge fields valued in finite groups. We describe their generalization based on $p$-form gauge fields valued in finite abelian groups, as field theories extended to codimension 2.