From Moyal deformations to chiral higher-spin theories and to celestial algebras

TL;DR

This paper explores the connections between Moyal deformations, chiral higher-spin theories, and celestial algebras, revealing structural insights and new algebraic deformations relevant to holography and scattering amplitudes.

Contribution

It establishes links between Moyal deformations and chiral higher-spin theories, and introduces celestial algebras for these theories, advancing understanding of their algebraic and holographic structures.

Findings

Moyal deformations relate to vanishing tree-level scattering amplitudes.

Deformation of celestial algebras corresponds to Moyal-deformed theories.

Introduces celestial algebras for various chiral higher-spin theories.

Abstract

We study the connection of Moyal deformations of self-dual gravity and self-dual Yang-Mills theory to chiral higher-spin theories, and also to deformations of operator algebras in celestial holography. The relation to Moyal deformations illuminates various aspects of the structure of chiral higher-spin theories. For instance, the appearance of the self-dual kinematic algebra in all the theories considered here leads via the double copy to vanishing tree-level scattering amplitudes. Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop algebra of $W_{\wedge}$, and we obtain here the analogous deformation of a Kac-Moody algebra corresponding to Moyal-deformed self-dual Yang-Mills theory. We also introduce the celestial algebras for various chiral higher-spin theories.