On-Shell Diagrams for N = 8 Supergravity Amplitudes

Understand

We define recursion relations for N = 8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar 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 N = 4 theory.
• This implies non-trivial identities for non-planar diagrams as well as interesting relations between the N = 4 and N = 8 theories.
• We show that the on-shell diagrams of N = 8 supergravity obey equivalence relations analogous to those of N = 4 super-Yang-Mills, and we develop a systematic algorithm for reading off Grassmannian integral formulae directly from the on-shell diagrams.