The chiral anomaly of the free fermion in functorial field theory
- When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.
| Author details: | Matthias LudewigORCiDGND, Saskia RoosORCiD |
|---|---|
| DOI: | https://doi.org/10.1007/s00023-020-00893-6 |
| ISSN: | 1424-0637 |
| ISSN: | 1424-0661 |
| Title of parent work (English): | Annales Henri Poincaré : a journal of theoretical and mathematical physics |
| Publisher: | Springer International Publishing AG |
| Place of publishing: | Cham (ZG) |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/02/08 |
| Publication year: | 2020 |
| Release date: | 2023/03/27 |
| Volume: | 21 |
| Issue: | 4 |
| Number of pages: | 43 |
| First page: | 1191 |
| Last Page: | 1233 |
| Funding institution: | Projekt DEAL; Max Planck Foundation Foundation CELLEX; ARCAustralian; Research Council [FL170100020]; Hausdorff Center of Mathematics in Bonn; DFGGerman Research Foundation (DFG)European Commission [SPP2026] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Hybrid Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
