The caloron correspondence and higher string classes for loop groups

Abstract

We review the caloron correspondence between $G$-bundles on $M\times S^1$ and $\Omega G$-bundles on $M$, where $\Omega G$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $\Omega G$-bundles, called string classes, by transgression of characteristic classes of $G$-bundles. These generalise the string class of Killingback to higher dimensional cohomology.

21 pages. Author addresses added

References in corpus (4)

• Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
• T-Duality as a Duality of Loop Group Bundles
• Circle actions, central extensions and string structures
• Chern-Weil calculus extended to a class of infinite dimensional manifolds

Cited by in corpus (8)

• The general caloron correspondence
• Dirac Geometry of the Holonomy Fibration
• A Geometric Model for Odd Differential K-theory
• Circle actions, central extensions and string structures
• On the energy spectrum of Yang--Mills instantons over asymptotically locally flat spaces
• Equivariant, string and leading order characteristic classes associated to fibrations
• The Caloron Correspondence and Odd Differential K-theory
• Universal string classes and equivariant cohomology