The Grassmannian Origin Of Dual Superconformal Invariance

TL;DR

This paper demonstrates that dual superconformal invariance in N=4 SYM scattering amplitudes can be understood through a Grassmannian geometric framework, connecting momentum variables and momentum twistors.

Contribution

It reveals that the Grassmannian integral formulation naturally encodes dual superconformal invariance and provides a simple derivation of the momentum-twistor space formula.

Findings

Dual superconformal invariance is manifest in the Grassmannian formulation.

A change of variables relates G(k,n) to G(k-2,n), corresponding to momentum twistors.

The approach offers a geometric understanding of symmetries in N=4 SYM amplitudes.

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.