Gravity, Twistors and the MHV Formalism

TL;DR

This paper derives gravitational MHV amplitudes using twistor theory, providing a new twistor action framework for perturbative gravity and supergravity, connecting spacetime and twistor data.

Contribution

It introduces a twistor-based formalism for gravity MHV amplitudes and constructs a twistor action for the MHV diagram approach to perturbative gravity.

Findings

Derived a spacetime formula for positive to negative helicity graviton scattering.

Expressed gravitational MHV amplitudes in twistor data, reproducing known results.

Extended the formalism to supergravity theories, including N=4 and N=8.

Abstract

We give a self-contained derivation of the MHV amplitudes for gravity and use the associated twistor generating function to define a twistor action for the MHV diagram approach to gravity. Starting from a background field calculation on a spacetime with anti self-dual curvature, we obtain a simple spacetime formula for the scattering of a single, positive helicity linearized graviton into one of negative helicity. Re-expressing our integral in terms of twistor data allows us to consider a spacetime that is asymptotic to a superposition of plane waves. Expanding these out perturbatively yields the gravitational MHV amplitudes of Berends, Giele & Kuijf. We go on to take the twistor generating function off-shell at the perturbative level. Combining this with a twistor action for the anti self-dual background, we obtain a twistor action for the MHV diagram approach to perturbative gravity. We finish by extending these results to supergravity, in particular N=4 and N=8.