A rigorous construction of the supersymmetric path integral associated to a compact spin manifold
- 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.
| Author details: | Florian HanischGND, Matthias LudewigORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s00220-022-04336-7 |
| ISSN: | 0010-3616 |
| ISSN: | 1432-0916 |
| Title of parent work (English): | Communications in mathematical physics |
| Publisher: | Springer |
| Place of publishing: | Berlin ; Heidelberg |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/05/01 |
| Publication year: | 2022 |
| Release date: | 2024/01/03 |
| Volume: | 391 |
| Issue: | 3 |
| Number of pages: | 31 |
| First page: | 1209 |
| Last Page: | 1239 |
| Funding institution: | Max-Planck-Institute for Gravitational Physics in Potsdam; (Albert-Einstein-Institute); Max-PlanckInstitute for Mathematics in; Bonn; Institute for Mathematics at the University of Potsdam;; Max-Planck-Foundation; ARC [FL170100020] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
| Peer review: | Referiert |
| Publishing method: | Open Access / Hybrid Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
