Celestial Operator Products of Gluons and Gravitons

TL;DR

The paper demonstrates that celestial OPEs for massless gluons and gravitons are highly constrained by an infinite set of asymptotic symmetries, including subleading and subsubleading soft theorems. By combining recursion relations from these soft symmetries with Mellin-transform analyses of collinear limits, the leading poles of all OPEs in tree-level Einstein-Yang-Mills theory are fixed in terms of Euler beta functions. The authors verify these symmetry-based results with explicit collinear calculations and extend the framework to include both incoming and outgoing states. The findings imply that celestial CFT data may tightly determine aspects of quantum gravity coupled to gauge fields, highlighting a beta-function structure for OPE coefficients and connections to conformally soft currents.

Abstract

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.