# Celestial Operator Product Expansions and w1+infinity Symmetry for All Spins

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated.  Poincare symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product.  These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space  tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w1+infinity.  In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w1+infinity on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from  higher-derivative non-minimal couplings of gluons and gravitons.

### Affiliation

Harvard University

Monica Pate