TY  - JOUR
A1  - Hanisch, Florian
A1  - Ludewig, Matthias
T1  - A rigorous construction of the supersymmetric path integral associated to a compact spin manifold
T2  - Communications in mathematical physics
N2  - 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 Guneysu and the second author. Our 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-Gaume, Atiyah, Bismut and Witten.
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/61813
SN  - 0010-3616
SN  - 1432-0916
VL  - 391
IS  - 3
SP  - 1209
EP  - 1239
PB  - Springer
CY  - Berlin ; Heidelberg
ER  -