Dual Superconformal Invariance, Momentum Twistors and Grassmannians

TL;DR

This paper explores how dual superconformal invariance in N=4 super Yang-Mills theory can be made explicit using momentum twistors, linking Grassmannian integrals to scattering amplitudes.

Contribution

It introduces a novel formulation of scattering amplitudes in momentum twistor space using Grassmannian integrals, distinct from previous twistor space approaches.

Findings

Tree amplitudes are generated by Grassmannian integrals in momentum twistor space.

Box coefficients can be expressed as integrals over cycles in the Grassmannian.

The approach connects with Hodges' polyhedral NMHV amplitude representation.

Abstract

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.