  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.
