On-shell diagrams for N $$ mathcal{N} $$ = 8 supergravity amplitudes

We define recursion relations for $$ mathcal{n} $$ = 8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar $$ mathcal{n} $$ = 4 super-yang-mills. although the recursion relations generically give rise to non-planar on-shell diagrams, we show that at tree-level the recursion can be chosen to yield only planar diagrams, the same diagrams occurring in the planar $$ mathcal{n} $$ = 4 theory. this implies non-trivial identities for non-planar diagrams as well as interesting relations between the $$ mathcal{n} $$ = 4 and $$ mathcal{n} $$ = 8 theories. we show that the on-shell diagrams of $$ mathcal{n} $$ = 8 supergravity obey equivalence relations analogous to those of $$ mathcal{n} $$ = 4 super-yang-mills, and we develop a systematic algorithm for reading off grassmannian integral formulae directly from the on-shell diagrams. we also show that the 1-loop 4-point amplitude of $$ mathcal{n} $$ = 8 supergravity can be obtained from on-shell diagrams.