Higher-spin self-dual Yang-Mills and gravity from the twistor space

Herfray, Yannick; Krasnov, Kirill; Skvortsov, Evgeny

Abstract

We lift the recently proposed theories of higher-spin self-dual Yang-Mills (SDYM) and gravity (SDGR) to the twistor space. We find that the most natural room for their twistor formulation is not in the projective, but in the full twistor space, which is the total space of the spinor bundle over the 4-dimensional manifold. In the case of higher-spin extension of the SDYM we prove an analogue of the Ward theorem, and show that there is a one-to-one correspondence between the solutions of the field equations and holomorphic vector bundles over the twistor space. In the case of the higher-spin extension of SDGR we show show that there is a one-to-one correspondence between solutions of the field equations and Ehresmann connections on the twistor space whose horizontal distributions are Poisson, and whose curvature is decomposable. These data then define an almost complex structure on the twistor space that is integrable.

Citation

Herfray, Y., Krasnov, K., & Skvortsov, E. (2023). Higher-spin self-dual Yang-Mills and gravity from the twistor space. Journal of High Energy Physics, 2023, Article 158. https://doi.org/10.1007/jhep01%282023%29158

• Journal Article Type: Article
• Acceptance Date: Jan 14, 2023
• Online Publication Date: Jan 27, 2023
• Publication Date: Jan 27, 2023
• Deposit Date: Apr 3, 2023
• Publicly Available Date: Apr 3, 2023
• Journal: Journal of High Energy Physics
• Electronic ISSN: 1029-8479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Article Number: 158
• DOI: https://doi.org/10.1007/jhep01%282023%29158
• Keywords: Higher Spin Symmetry, Higher Spin Gravity, Integrable Hierarchies
• Public URL: https://nottingham-repository.worktribe.com/output/16789717
• Publisher URL: https://link.springer.com/article/10.1007/jhep01(2023)158
• Additional Information: Received: 31 October 2022; Revised: 10 January 2023; Accepted: 14 January 2023; First Online: 27 January 2023