Conformal and Einstein gravity from twistor actions

We use the embedding of Einstein gravity with cosmological constant intoconformal gravity as a basis for using the twistor action for conformal gravityto obtain maximal-helicity-violating (MHV) scattering amplitudes not just forconformal gravity, but also for Einstein gravity on backgrounds with nonzerocosmological constant. The new formulae for the gravitational MHV amplitude with cosmological constant arise by summing Feynman diagrams using the matrix-tree theorem. We show that this formula is well-defined (i.e.,is independent of certain gauge choices) and that it non-trivially reproducesHodges’ formula for the MHV amplitude in the flat-space limit. We give apreliminary discussion of an MHV formalism for more general amplitudesobtained from the conformal gravity twistor action in an axial gauge. We alsosee that the embedding of Einstein data into the conformal gravity action canbe performed off-shell in twistor space to give a proposal for an Einsten twistoraction that automatically gives the same MHV amplitude. These ideas extendnaturally to N = 4 supersymmetry.