All $S$ invariant gluon OPEs on the celestial sphere

TL;DR

This paper classifies all possible $S$-invariant operator product expansions (OPEs) for positive helicity gluons on the celestial sphere and explores the associated null states, suggesting an infinite family of $S$-invariant gauge theories.

Contribution

It explicitly derives all $S$-invariant gluon OPEs on the celestial sphere and identifies null states, indicating a vast class of $S$-invariant gauge theories including known sectors.

Findings

All $S$-invariant gluon OPEs are explicitly written down.

Null states of the $S$ algebra are identified.

Evidence for an infinite class of $S$-invariant gauge theories, including MHV and self-dual Yang-Mills.

Abstract

$S$ algebra is an infinite dimensional Lie algebra which is known to be the symmetry algebra of some gauge theories. It is a "coloured version" of the $w_{1+\infty}$. In this paper we write down all possible $S$ invariant (celestial) OPEs between two positive helicity outgoing gluons and also find the Knizhnik-Zamolodchikov type null states for these theories. Our analysis hints at the existence of an infinite number of $S$ invariant gauge theories which include the (tree-level) MHV-sector and the self-dual Yang-Mills theory.