MHV-Vertices for Gravity Amplitudes

TL;DR

The paper develops a CSW-style MHV-vertex formalism for graviton amplitudes and proves its validity under a BCFW-like analytic shift, enabling NMHV gravity amplitudes to be expressed as sums of diagrams built from gravity MHV vertices connected by propagators. It provides explicit five-point and eight-point examples, proves the general MHV-vertex rules via a two-step recursion, and extends the construction to arbitrary $\mathrm{N^nMHV}$ amplitudes. The approach clarifies the twistor-space structure of gravity amplitudes and highlights connections to KLT relations, suggesting a path toward twistor-string-like descriptions of gravity. Overall, the work offers a concrete computational framework for gravity amplitudes that parallels the Yang-Mills CSW construction and motivates further exploration of gravity in twistor space.

Abstract

We obtain a CSW-style formalism for calculating graviton scattering amplitudes and prove its validity through the use of a special type of BCFW-like parameter shift. The procedure is illustrated with explicit examples.