The tree formula for MHV graviton amplitudes

We present and prove a formula for the MHV scattering amplitude of n gravitons at tree level. Some of the more interesting features of t he 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.