Ludewig, Matthias and Stoffel, Augusto (2021) A Framework for Geometric Field Theories and their Classification in Dimension One. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 17: 072. ISSN 1815-0659
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In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the output of our field theory to depend smoothly on the input. We then test our framework on the case of 1-dimensional field theories (with or without orientation) over a manifold M. Here the expectation is that such a field theory is equivalent to the data of a vector bundle over M with connection and, in the nonoriented case, the additional data of a nondegenerate bilinear pairing; we prove that this is indeed the case in our framework.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | field theory; vector bundles; bordism |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Jul 2022 05:54 |
| Last Modified: | 06 Jul 2022 05:54 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45696 |
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