# A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold

#### Autoren: Florian Hanisch, Matthias Ludewig (2022)

We give a rigorous construction of the path integral in 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. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Güneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem using supersymmetric path integrals, as investigated by Alvarez-Gaumé, Atiyah, Bismut and Witten.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
1209–1239
Band:
391

zur Übersicht der Publikationen