Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted p...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210223 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles / R. Herrera, N. Santana // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 40 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-210223 |
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Herrera, R. Santana, N. 2025-12-04T13:01:37Z 2019 Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles / R. Herrera, N. Santana // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C10; 53C25; 53C27; 58J60 arXiv: 1506.07681 https://nasplib.isofts.kiev.ua/handle/123456789/210223 https://doi.org/10.3842/SIGMA.2019.072 We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also introduce the Clifford monopole equations as a natural geometric generalization of the Seiberg-Witten equations. We show that they restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit non-trivial solutions on manifolds with special Riemannian holonomy. The first-named author would like to thank H. Baum and U. Bruzzo for their hospitality, as well as the International Centre for Theoretical Physics, the Institut des Hautes Études Scientifiques, and the Scuola Internazionale Superiore di Studi Avanzati for their hospitality and support. The authors would also like to thank Alexander Quintero for his very valuable insights, as well as the anonymous referees for their comments, which helped improve the paper. The first author was partially supported by grants from CONACyT, LAISLA (CONACyT-CNRS), INFN-Italy, and IMU Berlin Einstein Foundation, and the second author was partially supported by grants from CONACyT and LAISLA (CONACyT-CNRS). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles |
| spellingShingle |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles Herrera, R. Santana, N. |
| title_short |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles |
| title_full |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles |
| title_fullStr |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles |
| title_full_unstemmed |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles |
| title_sort |
spinorially twisted spin structures. ii: twisted pure spinors, special riemannian holonomy and clifford monopoles |
| author |
Herrera, R. Santana, N. |
| author_facet |
Herrera, R. Santana, N. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also introduce the Clifford monopole equations as a natural geometric generalization of the Seiberg-Witten equations. We show that they restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit non-trivial solutions on manifolds with special Riemannian holonomy.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210223 |
| citation_txt |
Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles / R. Herrera, N. Santana // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 40 назв. — англ. |
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| first_indexed |
2025-12-07T21:24:48Z |
| last_indexed |
2025-12-07T21:24:48Z |
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1850886260214726656 |