Gravity from Rational Curves

TL;DR

This paper introduces a new formula for all tree-level amplitudes in N=8 supergravity using rational maps to twistor space, exhibiting manifest supersymmetry and permutation symmetry, with verified results up to eight external states.

Contribution

It proposes a novel, conjectured formula for supergravity amplitudes based on rational curves in twistor space, unifying various known results and extending computational checks.

Findings

Correctly reproduces 3-point MHV-bar and n-point MHV amplitudes.

Reduces to Hodges' expression for MHV amplitudes.

Numerical validation up to eight external states at NMHV and NNMHV levels.

Abstract

This paper presents a new formula which is conjectured to yield all tree amplitudes in N=8 supergravity. The amplitudes are described in terms of higher degree rational maps to twistor space. The resulting expression has manifest N=8 supersymmetry and is manifestly permutation symmetric in all external states. It depends monomially on the infinity twistor that explicitly breaks conformal symmetry to Poincare. The formula has been explicitly checked to yield the correct amplitudes for the 3-point MHV-bar and for the n-point MHV, where it reduces to an expression of Hodges. We have also carried out numerical checks of the formula at NMHV and NNMHV level, for up to eight external states.