Gravity, Twistors and the MHV Formalism

We give a self-contained proof of the formula for the MHV amplitudes for gravity conjectured by Berends, Giele & Kuijf 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, the generating function provides the MHV vertices for the MHV diagram approach to perturbative gravity. We finish by extending these results to supergravity, in particular N = 4 and N = 8.