Categorical generalization of BF theory coupled to gravity

TL;DR

This paper introduces a categorical generalization of BF theory called BFCG, explores its relation to gravity, and proposes a new coupling approach that connects it to unimodular gravity, expanding the theoretical framework.

Contribution

It develops the BFCG (2BF) theory using category theory, linking it to gravity and unimodular gravity, and introduces new coupling methods involving volume forms.

Findings

BFCG can be deformed to produce general relativity.

A new coupling between BFCG and gravity is proposed using volume forms.

BF sequestered gravity is recovered in the abelian case with specific 2-group choices.

Abstract

We present a thorough introduction to the tools of category theory required for formulating gauge theories based on 2-connections. We provide a detailed construction of the categorical generalization of BF theory, dubbed BFCG, also known as 2BF. Similar to BF gravity, it is known that BFCG can be deformed to give general relativity. Here, we obtain an alternative relation between BFCG and gravity, which consists of coupling general relativity and BFCG by means of the volume form constructed out of the BFCG connections. The resulting theory, closely related to unimodular gravity, is a generalization of BF sequestered gravity not only in the sense that it adds new fields but also in that it allows for new choices for the volume form that is coupled to gravity. Furthermore, we show that BF sequestered gravity in the abelian case is recovered for a specific choice of the 2-group.