Circle actions, central extensions and string structures

Abstract

The caloron correspondence can be understood as an equivalence of categories between $G$-bundles over circle bundles and $LG{⋊}_{\rho }{S}^1$-bundles where $LG$ is the group of smooth loops in $G$. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an $LG{⋊}_{\rho }{S}^1$-bundle.

25 pages

References in corpus (2)

• The caloron correspondence and higher string classes for loop groups
• T-Duality as a Duality of Loop Group Bundles

Cited by in corpus (4)

• The caloron correspondence and higher string classes for loop groups
• The general caloron correspondence
• Bundle gerbes and moduli spaces
• Universal string classes and equivariant cohomology