Cartan geometry, supergravity, and group manifold approach

TL;DR

This paper advocates for the importance of Cartan geometry in understanding gauge theories of gravity and supergravity, highlighting its conceptual connections and potential to unify different approaches.

Contribution

It provides a conceptual overview linking Cartan geometry with gauge theories of gravity and supergravity, fostering cross-disciplinary understanding.

Findings

Highlights the role of Cartan geometry in gauge theories of gravity.

Connects group manifold approach to supergravity with Cartan supergeometry.

Serves as a bridge between physics and mathematics communities.

Abstract

We make a case for the unique relevance of Cartan geometry for gauge theories of gravity and supergravity. We introduce our discussion by recapitulating historical threads, providing motivations. In a first part we review the geometry of classical gauge theory, as a background for understanding gauge theories of gravity in terms of Cartan geometry. The second part introduces the basics of the group manifold approach to supergravity, hinting at the deep rooted connections to Cartan supergeometry. The contribution is intended, not as an extensive review, but as a conceptual overview, and hopefully a bridge between communities in physics and mathematics.