Gravity, Twistors and the MHV Formalism

Details Gravity, Twistors and the MHV Formalism Gravity, Twistors and the MHV Formalism

2008-08-28

arxiv.org/abs/0808.3907v2

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 3 figures. Minor typos corrected, some clarification added

Scientific paper

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.

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