Moyal deformations, $W_{1+\infty }$ and celestial holography

Abstract

We consider the Moyal deformation of self-dual gravity. In the conformal primary basis, holomorphic collinear limits of the amplitudes of this theory show that it enjoys a perturbatively exact symmetry algebra $L{W}_{\wedge }$ that generalises $L{w}_{\wedge }$, the loop algebra of the wedge algebra of $w_{1+\infty }$, which appears in self-dual gravity.

Some argument slightly changed, references added