Dual Superconformal Invariance, Momentum Twistors and Grassmannians

Dual superconformal invariance has recently emerged as a hidden symmetry of
planar scattering amplitudes in N=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 delta-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.