A Link Representation for Gravity Amplitudes

TL;DR

This paper introduces a new link representation for all tree-level amplitudes in N=8 supergravity, expressing them as contour integrals over link variables that preserve key symmetries and suggest a path toward Grassmannian formulations.

Contribution

It derives a novel link representation for supergravity amplitudes that maintains symmetries and connects to Grassmannian integral approaches.

Findings

Explicit link representation as contour integrals

Manifest supersymmetry, parity, and permutation invariance

Potential for generalization to Grassmannian contour integrals

Abstract

We derive a link representation for all tree amplitudes in N=8 supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally expressed in terms of determinants, or equivalently tree diagrams. Important symmetries of the amplitude, such as supersymmetry, parity and (partial) permutation invariance, are kept manifest in the formulation. We also comment on rewriting the formula in a GL(k)-invariant manner, which may serve as a starting point for the generalization to possible Grassmannian contour integrals.