Title: Classical and Quantum Integrability in Self-Dual Gravity

Abstract: This talk will concentrate on an intriguing example of a 4d integrable theory: self-dual gravity. I will explain how its classical integrability is realised in the existence of an infinite dimensional hidden symmetry algebra, or celestial chiral algebra. This governs the universal holomorphic surface defect which can couple to the twistor uplift of self-dual gravity. At the quantum level, this twistor uplift is anomalous and the quantum corrected chiral algebra fails to be associative. I will present a number of methods of cancelling the anomaly, leading to consistent quantum corrected hidden symmetry algebras. Finally, I will explore how this story is modified on one of the simplest non-trivial examples of a self-dual Ricci flat background: the Eguchi-Hanson gravitational instanton.

This talk is based on collaborations with Simon Heuveline, Atul Sharma and David Skinner.