Celestial operator products of gluons and gravitons

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.

Automated summary

The operator product expansion on the celestial sphere of conformal primary gluons and gravitons reveals recursion relations between operators with conformal weights differing by half-integers. For tree-level Einstein-Yang-Mills theory, these recursion relations tightly constrain the leading celestial OPE coefficients, which are completely determined by the Euler beta function. The poles in the beta functions are associated with conformally soft currents.