Conformal blocks from celestial graviton amplitudes

TL;DR

This paper introduces an analytic celestial graviton correlator with desirable properties, computes its conformal block decomposition, and reveals a double copy structure relating it to gluon amplitudes.

Contribution

It proposes a new analytic celestial graviton correlator, computes its conformal block decomposition, and uncovers a double copy relation to gluon amplitudes.

Findings

The correlator is analytic and has distributional support.

The conformal block decomposition is explicitly performed.

A double copy structure relating graviton and gluon amplitudes is found.

Abstract

Four-point gluon and graviton correlators in celestial holography are famously non-analytic, having distributional support. In this work, we propose an alternative graviton correlator that is analytic and displays several desirable properties. We compute the four-point correlator involving one graviton shadow operator and three graviton primary operators from the celestial four-point graviton amplitudes at tree-level. We perform the conformal block decomposition for the shadow correlator in the compatible channel. For the case when the shadow operator is conformally soft, we compute the single-valued completion of the shadow correlator and perform the conformal block decomposition of the single-valued shadow correlator in all channels. We find an integral representation of the single-valued shadow correlator, which allows us to invert the shadow transform to find the single-valued celestial graviton amplitude. We study various properties of the single-valued celestial graviton amplitude. Interestingly, it exhibits a double copy structure in relation to its counterpart gluon amplitude.