The Tree Formula for MHV Graviton Amplitudes

TL;DR

This paper introduces a new, explicit formula for tree-level MHV graviton scattering amplitudes that is symmetric, free of cyclic ordering references, and exhibits favorable large-z behavior, with a proof based on complex analysis.

Contribution

It provides the first proof of a gravitational MHV amplitude formula that is symmetric, manifestly gravitational, and relies on complex analysis rather than brute-force identities.

Findings

The formula is symmetric under S_{n-2} permutations.

It exhibits O(1/z^2) large-z behavior term-by-term.

The link representation in twistor space reveals non-obvious cancellations.

Abstract

We present and prove a formula for the MHV scattering amplitude of n gravitons at tree level. Some of the more interesting features of the formula, which set it apart as being significantly different from many more familiar formulas, include the absence of any vestigial reference to a cyclic ordering of the gravitons--making it in a sense a truly gravitational formula, rather than a recycled Yang-Mills result, and the fact that it simultaneously manifests both S_{n-2} symmetry as well as large-z behavior that is O(1/z^2) term-by-term, without relying on delicate cancellations. The formula is seemingly related to others by an enormous simplification provided by O(n^n) iterated Schouten identities, but our proof relies on a complex analysis argument rather than such a brute force manipulation. We find that the formula has a very simple link representation in twistor space, where cancellations that are non-obvious in physical space become manifest.