The general caloron correspondence

TL;DR

This paper develops a comprehensive framework for the caloron correspondence applicable to automorphism groups of principal G-bundles, enabling the definition of characteristic classes with explicit differential form representatives.

Contribution

It extends the caloron correspondence to general automorphism groups of principal G-bundles, including gauge groups, and computes explicit differential form representatives.

Findings

Defined characteristic classes for gauge group bundles.

Computed explicit differential form representatives.

Extended caloron correspondence to arbitrary automorphism groups.

Abstract

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.