Gravity, Twistors and the MHV Formalism

Journal article

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 and 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.

Authors: Mason, L; Skinner, D

• Publication status: Published
• Journal: Commun.Math.Phys.
• Volume: 294
• Issue: 3
• Pages: 827-862
• Publication date: 2008-08-28
• DOI: 10.1007/s00220-009-0972-4
• EISSN: 1432-0916
• ISSN: 0010-3616
• Keywords: hep-th; gr-qc; math.DG