Tree-Level Amplitudes in N=8 Supergravity

TL;DR

This paper develops an explicit algorithm to compute all tree-level amplitudes in N=8 supergravity, extending techniques from N=4 super Yang-Mills by squaring dual superconformal invariants and adding gravity-specific factors.

Contribution

It introduces a novel recursive algorithm for N=8 supergravity amplitudes, generalizing the N=4 super Yang-Mills structure with new modifications.

Findings

Explicit formulas for all NMHV, NNMHV, NNNMV amplitudes

Unified nested sum structure for graviton amplitudes

Extension of superconformal invariants from N=4 to N=8 superspace

Abstract

We present an algorithm for writing down explicit formulas for all tree amplitudes in N=8 supergravity, obtained from solving the supersymmetric on-shell recursion relations. The formula is patterned after one recently obtained for all tree amplitudes in N=4 super Yang-Mills which involves nested sums of dual superconformal invariants. We find that all graviton amplitudes can be written in terms of exactly the same structure of nested sums with two modifications: the dual superconformal invariants are promoted from N=4 to N=8 superspace in the simplest manner possible--by squaring them--and certain additional non-dual conformal gravity dressing factors (independent of the superspace coordinates) are inserted into the nested sums. To illustrate the procedure we give explicit closed-form formulas for all NMHV, NNMHV and NNNMV gravity superamplitudes.