Dual superconformal invariance, momentum twistors and Grassmannians

Abstract

Dual superconformal invariance has recently emerged as a hidden symmetry of planar scattering amplitudes in = 4 super Yang-Mills theory. This symmetry can be made manifest by expressing amplitudes in terms of 'momentum twistors', as opposed to the usual twistors that make the ordinary superconformal properties manifest. The relation between momentum twistors and on-shell momenta is algebraic, so the translation procedure does not rely on any choice of space-time signature. We show that tree amplitudes and box coefficients are succinctly generated by integration of holomorphic δ-functions in momentum twistors over cycles in a Grassmannian. This is analogous to, although distinct from, recent results obtained by Arkani-Hamed et al. in ordinary twistor space. We also make contact with Hodges' polyhedral representation of NMHV amplitudes in momentum twistor space. © 2009 SISSA.