Celestial operator product expansions and w1+∞ symmetry for all spins

A bstract The operator product expansion of massless celestial primary operators arbitrary spin is investigated. Poincaré symmetry found to imply a set recursion relations on the coefficients leading singular terms at tree-level in holomorphic limit. constraints are solved by an Euler beta function with arguments that depend simply right-moving conformal weights product. These symmetry-derived shown not only match precisely those arising from momentum-space collinear limits, but also obey infinite number additional transformations respect algebra w 1+ ∞ . In minimally-coupled gravitational theories, currents constructed light transforms conformally soft gravitons and generate action 1+∞ primaries. Results include for fermions as well higher-derivative non-minimal couplings gluons gravitons.