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

Journal of High Energy Physics

Regular Article - Theoretical Physics

Yannick Herfray¹  Kirill Krasnov²  Evgeny Skvortsov³ 

[1] Institut Denis Poisson UMR 7013, Université de Tours, Parc de Grandmont, 37200, Tours, France;School of Mathematical Sciences, University of Nottingham, NG7 2RD, Nottingham, UK;Service de Physique de l’Univers, Champs et Gravitation, Université de Mons, 20 place du Parc, 7000, Mons, Belgium;

关键词: Higher Spin Symmetry;    Higher Spin Gravity;    Integrable Hierarchies;   

DOI  :  10.1007/JHEP01(2023)158

 received in 2022-10-31, accepted in 2023-01-14,  发布年份 2023

来源: Springer

【 摘 要 】

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.

【 授权许可】

Unknown   
© The Author(s) 2023