Geodesic
Super Wilson Loops and Holonomy on Supermanifolds
Communications in Mathematics, Tome 22 (2014) no. 2, pp. 185-211

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MR Zbl
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.
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.
Classification : 18F05, 53C29, 58A50
Keywords: supermanifolds; holonomy; group functor 
Groeger, Josua. Super Wilson Loops and Holonomy on Supermanifolds. Communications in Mathematics, Tome 22 (2014) no. 2, pp. 185-211. http://geodesic.mathdoc.fr/item/COMIM_2014_22_2_a5/
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     title = {Super {Wilson} {Loops} and {Holonomy} on {Supermanifolds}},
     journal = {Communications in Mathematics},
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     volume = {22},
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     mrnumber = {3303138},
     zbl = {1316.58004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2014_22_2_a5/}
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