All $S$ invariant gluon OPEs on the celestial sphere

Partha Paul; Raju Mandal; Sagnik Misra; Shamik Banerjee; Sudhakar Panda

All $S$ invariant gluon OPEs on the celestial sphere

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arxiv 2311.16796 v2 pith:KZTB3JOA submitted 2023-11-28 hep-th

Shamik Banerjee , Raju Mandal , Sagnik Misra , Sudhakar Panda , Partha Paul This is my paper

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keywords algebrainvarianttheoriescelestialgaugeinfiniteopesanalysis

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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.

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Holographic symmetry algebra for the MHV sector revisited
hep-th 2025-08 conditional novelty 6.0 of 10

In the MHV sector, the celestial symmetry algebra is a semidirect product of w_{1+∞} (or S) with an infinite Abelian algebra, whose null states supply the two missing KZ equations.

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