  $S$ 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.
