On-Shell Diagrams for N = 8 Supergravity Amplitudes

TL;DR

This paper extends on-shell diagram techniques from N=4 super-Yang-Mills to N=8 supergravity, deriving recursion relations, identities, and Grassmannian formulas, and computing the 1-loop 4-point amplitude.

Contribution

It introduces a systematic approach to construct and analyze N=8 supergravity amplitudes using on-shell diagrams, revealing new identities and relations with N=4 theory.

Findings

Tree-level recursion yields only planar diagrams in N=8 supergravity.

On-shell diagrams obey equivalence relations similar to N=4 super-Yang-Mills.

The 1-loop 4-point amplitude can be derived from on-shell diagrams.

Abstract

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. We also show that the 1-loop 4-point amplitude of N = 8 supergravity can be obtained from on-shell diagrams.