Address:
a Department of Mathematics and Statistics, Masaryk University, Kotlářská 267/2, 611 37, Brno, Czech Republic
b Department of Philosophy, University of Graz, Heinrichstraße 26/5, 8010 Graz, Austria
c Department of Physics, Mons University, UMONS, Service Physics of the Universe, Fields & Gravitation, 20 Place du Parc, 7000 Mons, Belgium
d DISAT, Politecnico di Torino, PoliTo, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
e Istituto Nazionale di Fisica Nucleare, Section of Torino, INFN, Via P. Giuria 1, 10125 Torino, Italy
f Grupo de Investigación en Física Teórica, GIFT, Concepción, Chile
E-mail: lucrezia.ravera@polito.it
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.
AMSclassification: primary 53Z05; secondary 58A32, 58A50, 83-01, 83E50, 83-03.
Keywords: Cartan geometry, group manifold, classical gauge field theory of gravity, Cartan supergeometry, supergroup manifold, supergravity.
DOI: 10.5817/AM2024-4-243