The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space

Abstract

We consider the twistor description of classical self-dual Einstein gravity in the presence of a defect operator wrapping a certain ${\mathbb{CP}}^1$. 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 $W(\mu )$-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 $W(\mu )$-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.

33 pages + 12 page appendix, 3 figures; v2: published in JHEP

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