The Grassmannian origin of dual superconformal invariance

Abstract

A dual formulation of the S Matrix for N=4 SYM has recently been presented, where all leading singularities of n-particle N^{k-2}MHV amplitudes are given as an integral over the Grassmannian G(k,n), with cyclic symmetry, parity and superconformal invariance manifest. In this short note we show that the dual superconformal invariance of this object is also manifest. The geometry naturally suggests a partial integration and simple change of variable to an integral over G(k-2,n). This change of variable precisely corresponds to the mapping between usual momentum variables and the "momentum twistors" introduced by Hodges, and yields an elementary derivation of the momentum-twistor space formula very recently presented by Mason and Skinner, which is manifestly dual superconformal invariant. Thus the G(k,n) Grassmannian formulation allows a direct understanding of all the important symmetries of N=4 SYM scattering amplitudes.