Double Copy for Celestial Amplitudes

TL;DR

This paper develops a method to extend the double copy relation, known in gauge theory and gravity amplitudes, to celestial amplitudes expressed in a conformal basis, revealing new structures in holographic flat space.

Contribution

It introduces a generalized double copy procedure for celestial amplitudes, involving differential operators, and demonstrates its validity for three and four-point cases.

Findings

Established a celestial double copy procedure using differential operators.

Demonstrated the method for three and four-point amplitudes.

Provided an argument for all-multiplicity validity.

Abstract

Celestial amplitudes which use conformal primary wavefunctions rather than plane waves as external states offer a novel opportunity to study properties of amplitudes with manifest conformal covariance and give insight into a potential holographic celestial CFT at the null boundary of asymptotically flat space. Since translation invariance is obscured in the conformal basis, features of amplitudes that heavily rely on it appear to be lost. Among these are the remarkable relations between gauge theory and gravity amplitudes known as the double copy. Nevertheless, properties of amplitudes reflecting fundamental aspects of the perturbative regime of quantum field theory are expected to survive a change of basis. Here we show that there exists a well-defined procedure for a celestial double copy. This requires a generalization of the usual squaring of numerators which entails first promoting them to generalized differential operators acting on external wavefunctions, and then squaring them. We demonstrate this procedure for three and four point celestial amplitudes, and give an argument for its validity to all multiplicities.