# Supersymmetric Path Integrals I: Differential Forms on the Loop Space

#### Autoren: Florian Hanisch, Matthias Ludewig (2017)

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.

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