Topological Higher Gauge Theory - from BF to BFCG theory

TL;DR

This paper explores higher gauge theories in 3 and 4 dimensions, constructing topological models and relating them to known theories like 3D gravity and 4D BF-theory with topological matter.

Contribution

It introduces discrete state sum models for higher gauge theories and connects them to existing continuum Lagrangian formulations, expanding the understanding of topological higher gauge theories.

Findings

Constructed topological higher gauge theories as discrete state sum models.

Connected these models to known theories such as 3D gravity and 4D BF-theory.

Provided continuum counterparts under certain conditions.

Abstract

We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature: the SigmaPhiEA-model of 3-dimensional gravity coupled to topological matter, and also a 4-dimensional model of BF-theory coupled to topological matter.