2015/07/06 by Mickler, Ryan · 1 citation
#58J28 #81T13 #81T45 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1507.01626
We consider Chern-Simons theory on 3-manifold M that is the total space of a circle bundle over a 2d base Σ. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with structure group given by the full affine level k central extension of the loop group LG. The space of fields of this 2d theory is naturally symplectic, and this provides a new formulation of a result of Beasley-Witten about the equivariant localization of the Chern-Simons path integral. The main tool that we employ is the Caloron correspondence, originally due to Murray-Garland, that relates the space of gauge fields on M with a certain enlarged space of connections on an equivariant version of the loop space of the G-bundle. We show that the symplectic structure that Beasley-Witten found is related to a looped version of the Atiyah-Bott construction in 2-dimensional Yang-Mills theory. We also show that Wilson loops that wrap a single circle fiber are also described very naturally in this framework.