We construct an integral map for differential forms on the loop space of Riemannian spin manifolds.
For example, Bismut-Chern character forms are integrable with respect to this map, with their integrals
given by indices of Dirac operators. This provides a rigorous background for supersymmetry proofs of
the Atiyah-Singer Index theorem.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/3946