Cartan geometry, supergravity and group manifold approach

François, Jordan ; Ravera, Lucrezia

Archivum mathematicum, Tome 60 (2024) no. 4, pp. 243-281

Abstract (VO)

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.

Détail

DOI : 10.5817/AM2024-4-243

Classification : 53Z05, 58A32, 58A50, 83-01, 83-03, 83E50
Keywords: Cartan geometry; group manifold; classical gauge field theory of gravity; Cartan supergeometry; supergroup manifold; supergravity

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