Celestial Leaf Amplitudes

TL;DR

This paper demonstrates that celestial amplitudes can be decomposed into AdS$_3$-Witten diagrams, revealing their singularity structure and showing how the full amplitude relates to residues at specific conformal weights, aligning with known formulas.

Contribution

It introduces a decomposition of celestial amplitudes into leaf subamplitudes linked to AdS$_3$-Witten diagrams and clarifies their singularity and residue structure for the three-point MHV amplitude.

Findings

Leaf subamplitudes are smooth except for light-cone singularities.

Full celestial amplitude is the residue at a specific conformal weight pole.

The amplitude matches the Mellin transform of the Parke-Taylor formula.

Abstract

Celestial amplitudes may be decomposed as weighted integrals of AdS$_3$-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.