Note on graviton MHV amplitudes

TL;DR

This paper derives two on-shell formulas expressing n-graviton MHV amplitudes as sums of squares of n-gluon MHV amplitudes. One formula arises from gravity recursion relations with a [2,1⟩ shift, while a second BGK-inspired form is obtained by reframing a BGK expression to emphasize a gauge-theory-squared structure. The results are checked against KLT relations for low n, connected to qmc’s graviton MHV formula, and shown to align with BGK in a similar squared-amplitude form. A modest non-MHV result for anti-MHV 5-point gravity amplitudes is also presented, highlighting the greater complexity of extending these methods beyond MHV. Overall, the work advances a field-theory derivation path toward MHV gravity amplitudes as sums of squared gauge-theory amplitudes, with implications for simplifying gravity calculations and approaching general-KLT-type relations.

Abstract

Two new formulas which express n-graviton MHV tree amplitudes in terms of sums of squares of n-gluon amplitudes are discussed. The first formula is derived from recursion relations. The second formula, simpler because it involves fewer permutations, is obtained from the variant of the Berends, Giele, Kuijf formula given in Arxiv:0707.1035.