Rubens Longhi (UP)
In this paper, we construct an integral map for differential forms on the loop space of Riemannian spin manifolds. In particular, the even and odd Bismut-Chern characters are integrable by this map, with their integrals given by indices of Dirac operators. We also show that our integral map satisfies a version of the localization principle in equivariant cohomology. This should provide a rigorous background for supersymmetry proofs of the Atiyah-Singer Index theorem.