N=7 On-shell diagrams and supergravity amplitudes in momentum twistor space

We derive an on-shell diagram recursion for tree-level scattering amplitudes in 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 N = 7 R-invariants analogous to those of 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.