On-shell recursion relations for gravity

TL;DR

This paper demonstrates that graviton tree amplitudes can be computed using BCFW recursion relations by showing their good behavior under complex momentum shifts, providing an alternative proof and revealing hidden cancellations.

Contribution

It extends the proof that gravity amplitudes are constructible via BCFW recursion, highlighting the role of auxiliary relations in exposing cancellations.

Findings

Gravity tree amplitudes are well-behaved under large complex deformations.

BCFW recursion relations can be applied to gravity amplitudes using such shifts.

Hidden cancellations in gravity amplitudes become manifest through auxiliary recursion relations.

Abstract

We extend the argument presented by Benincasa, Boucher-Veronneau, and Cachazo to show that graviton tree amplitudes are well behaved under large complex deformations of the momenta of a pair of like-helicity gravitons. This shows that BCFW recursion relations for gravity amplitudes can be constructed using such shifts, providing an alternative proof to the recent one by Arkani-Hamed and Kaplan. By using auxiliary recursion relations the cancellations which are hidden when using covariant Feynman diagrams become manifest.