New Variables For Graviton Scattering Amplitudes

TL;DR

This paper introduces the S variables, a new set of kinematic variables for gravity theories, simplifying on-shell constraints and providing new insights into graviton scattering amplitudes.

Contribution

The paper presents the S variables, which trivialize on-shell constraints in gravity and relate to Grassmannian geometry, offering a new framework for analyzing graviton scattering.

Findings

S variables simplify on-shell constraints in gravity

They relate to Grassmannian geometry and momentum twistors

They enable a new, reference-free expression for soft factors and MHV amplitudes

Abstract

Motivated by the success of Hodges' momentum twistor variables in planar Yang-Mills, in this note we introduce a set of new variables, the S variables, which are tailored for gravity (or more generally for theories without color ordering). The S variables trivialize all on-shell constraints on kinematic data and momentum conservation while keeping permutation invariance. We explicitly show the relation between the S variables and the spinor-helicity variables as well as the connection to momentum twistors. The S variables can be nicely understood using the geometry of Grassmannians and are determined by a 2-plane and a 4-plane in C^n, with n the number of the particles. As an illustration of their utility, we use the S variables to present a reference-free form of soft factors and tree level MHV amplitudes of gravity which is obtained by using the recent formula given by Hodges.