A simple formula for gravitational MHV amplitudes

TL;DR

The paper delivers a simple, determinant-based formula for the n-point tree-level gravitational MHV amplitude that makes S_n symmetry manifest and builds on soft-factor phase structures. It rewrites the amplitude in terms of a symmetric matrix of gravitational soft factors, with an equivalent minor-determinant representation that satisfies a Hodges-style recursion. The work also connects to momentum-twistor space by showing the corresponding numerator, N_n, is a polynomial, and discusses computational advantages over previous BGK/Mason-Skinner expressions. Overall, it clarifies the structural simplicity of gravitational scattering and points toward broad generalizations beyond MHV amplitudes.

Abstract

A simple formula is given for the n-field tree-level MHV gravitational amplitude, based on soft limit factors. It expresses the full S_n symmetry naturally, as a determinant of elements of a symmetric (n \times n) matrix.