Cartan geometry, supergravity and group manifold approach

Jordan François; Lucrezia Ravera

Archivum Mathematicum (2024)

  • Volume: 060, Issue: 4, page 243-281
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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François, Jordan, and Ravera, Lucrezia. "Cartan geometry, supergravity and group manifold approach." Archivum Mathematicum 060.4 (2024): 243-281. <http://eudml.org/doc/299459>.

@article{François2024,
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.},
author = {François, Jordan, Ravera, Lucrezia},
journal = {Archivum Mathematicum},
keywords = {Cartan geometry; group manifold; classical gauge field theory of gravity; Cartan supergeometry; supergroup manifold; supergravity},
language = {eng},
number = {4},
pages = {243-281},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Cartan geometry, supergravity and group manifold approach},
url = {http://eudml.org/doc/299459},
volume = {060},
year = {2024},
}

TY - JOUR
AU - François, Jordan
AU - Ravera, Lucrezia
TI - Cartan geometry, supergravity and group manifold approach
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 060
IS - 4
SP - 243
EP - 281
AB - 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.
LA - eng
KW - Cartan geometry; group manifold; classical gauge field theory of gravity; Cartan supergeometry; supergroup manifold; supergravity
UR - http://eudml.org/doc/299459
ER -

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