$\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space

TL;DR

This paper develops an on-shell diagram recursion for tree-level supergravity amplitudes in $ $N=7, using Grassmannian integrals and momentum twistors, extending previous momentum twistor space results to non-MHV amplitudes.

Contribution

It introduces a novel recursion and Grassmannian integral formulation for $ $N=7 supergravity amplitudes in momentum twistor space, generalizing Hodges' work to non-MHV cases.

Findings

Recast five and six-point NMHV amplitudes in terms of $ $N=7 R-invariants.

Made cancellation of spurious poles more transparent.

Defined momentum twistors with respect to different orderings of external momenta.

Abstract

We derive an on-shell diagram recursion for tree-level scattering amplitudes in $\mathcal{N}=7$ supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of $\mathcal{N}=7$ R-invariants analogous to those of $\mathcal{N}=4$ super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of the external momenta.