Hanisch, Florian and Ludewig, Matthias (2022) A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 391 (3). pp. 1209-1239. ISSN 0010-3616, 1432-0916
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | INDEX THEOREM; QUANTUM-MECHANICS; CHERN CHARACTER; CYCLIC HOMOLOGY; LOOP-SPACES; FORMULAS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Feb 2024 13:29 |
| Last Modified: | 05 Feb 2024 13:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57193 |
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