Construction and examples of higher gauge theories

TL;DR

This paper constructs higher gauge theories using category theory, generalizing BF models to 2BF and 3BF models, and demonstrates their potential to unify various fundamental fields with gravity.

Contribution

It introduces a framework for higher gauge theories with 2- and 3-groups, providing explicit actions that unify matter fields with gravity.

Findings

Constructed higher gauge theories as generalizations of BF models.

Demonstrated the coupling of matter fields to gravity within this framework.

Highlighted the potential for unification of fundamental interactions.

Abstract

We provide several examples of higher gauge theories, constructed as generalizations of a BF model to 2BF and 3BF models with constraints. Using the framework of higher category theory, we introduce appropriate 2-groups and 3-groups, and construct the actions for the corresponding constrained 2BF and 3BF theories. In this way, we can construct actions which describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. Each action is naturally split into a topological sector and a sector with simplicity constraints. The properties of the higher gauge group structure opens up a possibility of a nontrivial unification of all fields.