CSW-like Expansion for Einstein Gravity

TL;DR

This paper develops a CSW-like expansion for gravity amplitudes using the link representation and global residue theorem, extending techniques from Yang-Mills theory to Einstein gravity and analyzing their validity.

Contribution

It introduces a novel CSW-like expansion for gravity amplitudes derived from recent link representation formulas, and verifies its consistency with existing Risager's expansion.

Findings

Successfully derived the expansion for 6- and 7-graviton amplitudes.

Confirmed the equivalence of one CSW term with Risager's diagram.

Identified the range of validity for the technique, failing at 12 particles.

Abstract

Using the recent formula presented by He and Cachazo-Mason-Skinner for the link representation of tree-level N=8 supergravity amplitudes, we derived a CSW-like expansion for the Next-to-MHV 6- and 7-graviton amplitudes by using the global residue theorem; a technique introduced originally for Yang-Mills amplitudes. We analytically checked the equivalence of one of the CSW terms and its corresponding Risager's diagram. For the remaining 6-graviton and all 7-graviton terms, we numerically checked the agreement with Risager's expansion. We showed that the conditions for the absence of contributions at infinity of the global residue theorem are satisfied for any number of particles. This means that our technique and Risager's should disagree starting at twelve particles where Risager's method is known to fail.