Transgression of gerbes to loop spaces
The talk is about the relation between gerbes over a smooth manifold M and principal bundles over the free loop space LM. The gerbes and the principal bundles have abelian structure groups and carry connections. Based on work of Brylinski and McLaughlin, I will describe a "transgression" functor that takes gerbes over M to principal bundles over LM. The goal of the talk is to specify conditions and additional structure for principal bundles over LM such that transgression is an equivalence of categories. Moreover, I will explicitly construct an inverse functor. As an application, we will revisit the relation between spin structures on M and loop space orientations.