Unified formalism for 6D superamplitudes based on a symplectic Grassmannian

Abstract

Recently, twistor-like formulations of tree amplitudes involving n massless particles have been proposed for various 6D supersymmetric theories. The formulas are based on two different forms of the scattering equations: one based on rational maps and the other based on polarized scattering equations. We show that both formulations can be interpreted in terms of a symplectic (or complex Lagrangian) Grassmannian, LG(n, 2n), and that they correspond to different ways of fixing the GL(n, ℂ) symmetry of LG(n, 2n). This provides an understanding of the equivalence of these different-looking formulas, and it leads to new twistor-like formulas for 6D superamplitudes.