Celestial Operator Products of Gluons and Gravitons

TL;DR

This paper investigates the operator product expansion of gluons and gravitons on the celestial sphere, revealing recursion relations that determine OPE coefficients in Einstein-Yang-Mills theory, linked to conformally soft currents.

Contribution

It demonstrates that asymptotic symmetries impose recursion relations that fully determine the leading celestial OPE coefficients in Einstein-Yang-Mills theory.

Findings

Recursion relations fix OPE coefficients in terms of Euler beta functions.

Poles in beta functions relate to conformally soft currents.

Results apply at tree-level in Einstein-Yang-Mills theory.

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.