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

TL;DR

This paper explores how the celestial chiral algebra of self-dual gravity deforms on Eguchi-Hanson space, revealing a loop algebra of a scaled W-algebra family, with implications for self-dual Yang-Mills.

Contribution

It introduces a deformation of the celestial chiral algebra for self-dual gravity on Eguchi-Hanson space, connecting it to a loop algebra of scaled W-algebras and extending to Yang-Mills.

Findings

Deformation of celestial chiral algebra to a loop algebra of W(μ)-algebras.

Construction of the algebra via Poisson brackets on deformed twistor space.

Verification through space-time calculations of gravitational splitting functions.

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.