Double Copy for Celestial Amplitudes.

Eduardo Casali,Andrea Puhm

doi:10.1103/physrevlett.126.101602

Abstract

Celestial amplitudes which use conformal primary wave functions 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 conformal field theory 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 wave functions 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.

Highlights

Introduction.—Scattering amplitudes are usually calculated using asymptotic states in a plane wave basis
Applying a Mellin transform to the energy of each external state in an amplitude amounts to a change in basis of the asymptotic states from plane waves to so-called conformal primary wave functions [1]
Amplitudes in which asymptotic states are in this conformal basis make conformal covariance manifest [2,3,4,5,6,7,8] and, offer a novel opportunity to study properties of amplitudes that may be obscured in a plane wave basis

Summary

Double Copy for Celestial Amplitudes

Celestial amplitudes which use conformal primary wave functions 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 conformal field theory at the null boundary of asymptotically flat space. 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 wave functions and squaring them. Of amplitudes that are expected to reflect fundamental properties of the perturbative regime of quantum field theory should survive a change of basis One such remarkable feature are the double copy relations [20], which state that gravitational amplitudes can be obtained by a well-defined “squaring” of gauge theory amplitudes. We propose a well-defined procedure for a celestial double copy This requires a generalization of the usual squaring of numerators to first promoting them to differential operators acting on external scalar wave functions and squaring them.

Published by the American Physical Society

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