• DOI:10.1063/5.0044343
• Corpus ID: 230438714

Super fiber bundles, connection forms, and parallel transport

@inproceedings{Eder2021SuperFB,
  title={Super fiber bundles, connection forms, and parallel transport},
  author={Konstantin Eder},
  year={2021}
}

• K. Eder
• Published 4 January 2021
• Mathematics, Physics

The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with a detailed introduction to super fiber bundles. We then introduce the concept of so-called relative supermanifolds as well as bundles and connections defined in these categories. Studying these objects turn out to be of utmost importance in order to, among other things, model anticommuting classical fermionic fields in mathematical physics. We then construct the parallel transport map corresponding to such connections and compare the results with those found by other means in the mathematical literature. Finally, applications of these methods to supergravity will be discussed such as the Cartan geometric formulation of Poincaré supergravity as well as the description of Killing vector fields and Killing spinors of super Riemannian manifolds arising from metric reductive super Cartan geometries. This paper can also be read as a companion paper of [22] studying a mathematical rigorous approach towards geometric supergravity.