A Grassmannian Etude in NMHV Minors

TL;DR

This paper proves the equivalence between two Grassmannian formulations for NMHV superamplitudes in N=4 Yang-Mills theory, extending previous results and clarifying their relationship.

Contribution

It provides a simple analytic proof of the equivalence between the Grassmannian and connected prescription formulas for all tree-level NMHV superamplitudes.

Findings

Established the equivalence for all tree-level NMHV superamplitudes.

Connected the deformed connected prescription to the Grassmannian integrand.

Extended previous six- and seven-point results to all cases.

Abstract

Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian formulation for the S-matrix of N=4 Yang-Mills as an integral over link variables. In parallel work, the connected prescription for computing tree amplitudes in Witten's twistor string theory has also been written in terms of link variables. In this paper we extend the six- and seven-point results of arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the equivalence between the two formulas for all tree-level NMHV superamplitudes. Also we note that a simple deformation of the connected prescription integrand gives directly the ACCK Grassmannian integrand in the limit when the deformation parameters equal zero.