Double Copy for Celestial Amplitudes

TL;DR

In the conformal primary (celestial) basis, translation invariance is not manifest, complicating the standard gauge–gravity double copy. The authors introduce a celestial double copy by promoting kinematic numerators to differential operators $\mathcal{K}_i^\mu = q_i^\mu e^{\partial_{\Delta_i}}$ that act on conformal wavefunctions and then squaring them to obtain gravity numerators, i.e. constructing $(\mathcal{N}_{YM})^2$ acting on scalar celestial amplitudes. They demonstrate the procedure explicitly at 3- and 4-point levels and argue its validity for arbitrary multiplicity, providing explicit expressions and showing how the naive approach fails due to spacetime-dependent momentum conservation. This work offers a principled, basis-invariant route to a celestial double copy, with potential implications for curved-space extensions, Ambitwistor-string connections, and insights into a celestial CFT description of flat-space holography.

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.