Manifolds with many Rarita-Schwinger fields
- The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
| Author details: | Christian BärORCiDGND, Rafe MazzeoORCiD |
|---|---|
| DOI: | https://doi.org/10.1007/s00220-021-04030-0 |
| ISSN: | 0010-3616 |
| ISSN: | 1432-0916 |
| Title of parent work (English): | Communications in mathematical physics |
| Publisher: | Springer |
| Place of publishing: | Berlin |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/04/16 |
| Publication year: | 2021 |
| Release date: | 2023/06/09 |
| Volume: | 384 |
| Issue: | 1 |
| Number of pages: | 16 |
| First page: | 533 |
| Last Page: | 548 |
| Funding institution: | Stanford Math Research Center; Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [SPP 2026]; NSFNational Science Foundation (NSF) [DMS-1608223] |
| 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 |
