Unified formalism for 6D superamplitudes based on a symplectic Grassmannian

Abstract

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, $$ \mathbbm{LG} $$ LG (n, 2n), and that they correspond to different ways of fixing the GL(n, ℂ) symmetry of $$ \mathbbm{LG} $$ 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.