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This article is cited in 3 scientific papers (total in 3 papers)
A Framework for Geometric Field Theories and their Classification in Dimension One
Matthias Ludewiga, Augusto Stoffelb a Universität Regensburg, Germany
b Universität Greifswald, Germany
Abstract:
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.
Keywords:
field theory, vector bundles, bordism.
Received: June 15, 2020; in final form July 12, 2021; Published online July 25, 2021
Citation:
Matthias Ludewig, Augusto Stoffel, “A Framework for Geometric Field Theories and their Classification in Dimension One”, SIGMA, 17 (2021), 072, 58 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1754 https://www.mathnet.ru/eng/sigma/v17/p72
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Abstract page: | 126 | Full-text PDF : | 18 | References: | 7 |
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