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Title: Super Wilson Loops and Holonomy on Supermanifolds (English)
Author: Groeger, Josua
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 22
Issue: 2
Year: 2014
Pages: 185-211
Summary lang: English
Category: math
Summary: The classical Wilson loop is the gauge-invariant trace of the parallel transport around a closed path with respect to a connection on a vector bundle over a smooth manifold. We build a precise mathematical model of the super Wilson loop, an extension introduced by Mason-Skinner and Caron-Huot, by endowing the objects occurring with auxiliary Graßmann generators coming from $S$-points. A key feature of our model is a supergeometric parallel transport, which allows for a natural notion of holonomy on a supermanifold as a Lie group valued functor. Our main results for that theory comprise an Ambrose-Singer theorem as well as a natural analogon of the holonomy principle. Finally, we compare our holonomy functor with the holonomy supergroup introduced by Galaev in the common situation of a topological point. It turns out that both theories are different, yet related in a sense made precise. (English)
Keyword: supermanifolds
Keyword: holonomy
Keyword: group functor
MSC: 18F05
MSC: 53C29
MSC: 58A50
idZBL: Zbl 1316.58004
idMR: MR3303138
Date available: 2015-01-27T09:44:34Z
Last updated: 2020-01-05
Stable URL:
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