Abstract
We consider the twistor description of classical self-dual Einstein gravity in the presence of a defect operator wrapping a certain ℂℙ1. The backreaction of this defect deforms the flat twistor space to that of Eguchi-Hanson space. We show that the celestial chiral algebra of self-dual gravity on the Eguchi-Hanson background is likewise deformed to become the loop algebra of a certain scaling limit of the family of W(μ)-algebras, where the scaling limit is controlled by the radius of the Eguchi-Hanson core. We construct this algebra by computing the Poisson algebra of holomorphic functions on the deformed twistor space, and check this result with a space-time calculation of the leading contribution to the gravitational splitting function. The loop algebra of a general W(μ)-algebra (away from the scaling limit) similarly arises as the celestial chiral algebra of Moyal-deformed self-dual gravity on Eguchi-Hanson space. We also obtain corresponding results for self-dual Yang-Mills.
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Acknowledgments
It is a pleasure to thank Kevin Costello, Nick Dorey, Maciej Dunajski, Sean Seet, Atul Sharma, Andy Strominger and Peter Wildemann for helpful conversations, and Atul Sharma for collaboration at an early stage of this project. We also thank the organisers of the workshop ‘Celestial Amplitudes and Flat Space Holography’ at the Corfu Summer Institute in 2022, and the conference ‘Quantum de Sitter Universe’ at the University of Cambridge in 2023. SH also thanks the organisers of the ’2023 Winter School in Mathematical Physics’ at the SwissMAP research station and particularly Tudor Dimofte for his interesting lectures and helpful conversations.
Declarations. Research of RB at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. The work of SH & DS has been supported in part by STFC HEP Theory Consolidated grant ST/T000694/1. SH is partly supported by St. John’s College, Cambridge. The authors have no competing interests to declare that are relevant to the content of this article. Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.
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Bittleston, R., Heuveline, S. & Skinner, D. The celestial chiral algebra of self-dual gravity on Eguchi-Hanson space. J. High Energ. Phys. 2023, 8 (2023). https://doi.org/10.1007/JHEP09(2023)008
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DOI: https://doi.org/10.1007/JHEP09(2023)008