Tree-Level Gravity Amplitudes at Infinity

TL;DR

This paper investigates the behavior of tree-level gravity amplitudes at infinity under various on-shell shifts, revealing unique factorization properties and implications for amplitude reconstruction.

Contribution

It introduces a detailed analysis of gravity amplitudes at infinity for different shifts, especially the $(n-2)$-line anti-holomorphic shift, uncovering novel factorization behaviors.

Findings

Amplitudes exhibit a peculiar factorization at infinity for certain shifts.

For some shifts, amplitudes evaluate to the same value on shifted kinematics.

The study extends to generalizations of anti-holomorphic shifts.

Abstract

In this note we study on-shell tree-level gravity amplitudes in the infinite momentum limit. In the case of the two-line BCFW shift, we have a famous improved behavior at infinity that allows for the amplitude to be reconstructed from the pole factorization. For other shifts, the poles at infinity are present and need to be considered, however general principles do not fix the residues of the amplitude on these poles. The web of all possible shifts is large, we focus primarily on a case of $(n{-}2)$-line anti-holomorphic shift, which also appears in the context of unitarity cuts of gravity loop integrands. We will find that for one class of shifts the gravity amplitudes at infinity exhibit a peculiar factorization property, quite different from the usual factorization on poles, while for other shifts, they evaluate to the same amplitude on shifted kinematics. We also discuss generalizations of our results to other anti-holomorphic shifts.