Scalar-Graviton Amplitudes and Celestial Holography

TL;DR

This paper calculates celestial correlators involving massive scalars and gravitons, revealing they are well-defined, non-divergent, and resemble standard CFT correlators, with modifications to soft theorems.

Contribution

It demonstrates that celestial correlators with a zero conformal dimension scalar depend solely on graviton coordinates and are free of divergences, aligning with CFT structures.

Findings

Celestial correlators are well-defined and non-divergent.

Correlators depend only on graviton coordinates when scalar dimension is zero.

Soft theorems are modified in this celestial framework.

Abstract

We compute scattering amplitudes involving one massive scalar and two, three, or four gravitons. We show that when the conformal dimension of the massive scalar is set to zero, the resulting celestial correlators depend {\it only} on the coordinates of the gravitons. Such correlators of gravitons are well-defined and do not suffer from divergences associated with the Mellin transform of usual graviton amplitudes. Moreover, they are non-distributional and take the form of standard CFT correlators. We show that they are consistent with the usual OPEs but the statement of the soft theorem is modified.