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 |
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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 |