The general caloron correspondence
  We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal $G$-bundle $Q$ over a manifold $X$, including the case of the gauge group of $Q$. These results are used to define characteristic classes of gauge group bundles. Explicit but complicated differential form representatives are computed in terms of a connection and Higgs field. 
Pedram Hekmati, Michael K. Murray and Raymond F. Vozzo
math.DG hep-th