A rigorous construction of the supersymmetric path integral associated to a compact spin manifold (Q2124217)

The authors give a rigorous construction of the path integral in \(\mathcal{N}=1/2\) supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler-Jones-Petrack. By means of the iterated integral map, the authors compare the path integral to the non-commutative loop space Chern character of Güneysu and the second author. This theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem for twisted Dirac operators using supersymmetric path integrals, as investigated by Alvarez-Gaumé, Atiyah, Bismut and Witten.