Categorical generalization of MacDowell Mansouri gravity coupled to Kalb Ramond fields

TL;DR

This paper extends the MacDowell-Mansouri gravity framework using strict 2-groups, leading to a categorical generalization that incorporates Kalb-Ramond fields and results in Einstein-Cartan theory with additional topological terms.

Contribution

It introduces a novel categorical generalization of the MacDowell-Mansouri theory using 2-groups, specifically the de Sitter 2-group, and explores two approaches to include Kalb-Ramond fields.

Findings

Constructed the de Sitter 2-group as a categorical generalization of ISO(4,1).

Developed two formulations: a Yang-Mills-type and a 2-BF theory, both leading to Einstein-Cartan with Kalb-Ramond fields.

Added symmetry breaking and constraints to obtain the desired gravitational theory with topological terms.

Abstract

In this work we generalize the MacDowell-Mansouri theory of gravity using strict 2-groups. To achieve this, we construct the categorical generalization of the ISO(4,1) group, which we call the de Sitter 2-group. We then proceed to generalize the MacDowell-Mansouri theory in two different ways. First, as a Yang-Mills-type theory, where the symmetry is explicitly broken to obtain an Einstein-Cartan theory coupled to Kalb-Ramond fields. And second, by using the categorical generalization of the BF theory, called 2-BF theory, which after the addition of some symmetry breaking and constraint terms gives the same Einstein-Cartan theory coupled to Kalb-Ramond fields plus some extra topological terms.