All OPEs invariant under the infinite symmetry algebra for gluons on the celestial sphere

Abstract

S algebra is an infinite-dimensional Lie algebra, which is known to be the symmetry algebra of some gauge theories. It is a “colored version” of the w1+∞. In this paper, we write down all possible S-invariant (celestial) operator product expansions 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) maximally helicity-violating sector and the self-dual Yang-Mills theory. Published by the American Physical Society 2024