Circle actions, central extensions and string structures

Details Circle actions, central extensions and string structures Circle actions, central extensions and string structures

2010-04-06

arxiv.org/abs/1004.0779v1

Int. J. Geom. Meth. Mod. Phys. 7:1065-1092, 2010

Mathematics

Differential Geometry

25 pages

Scientific paper

The caloron correspondence can be understood as an equivalence of categories
between $G$-bundles over circle bundles and $LG \rtimes_\rho S^1$-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 $LG \rtimes_\rho S^1$-bundle.

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