# Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian

## TL;DR

This paper unifies different 6D superamplitude formulations using a symplectic Grassmannian framework, revealing their equivalence and deriving new twistor-like formulas for supersymmetric theories.

## Contribution

It introduces a unified formalism based on the symplectic Grassmannian that explains the equivalence of existing scattering equations formulations in 6D superamplitudes.

## Key findings

- Unified interpretation of rational map and polarized scattering equations
- New twistor-like formulas for 6D superamplitudes
- Clarification of GL(n,C) symmetry fixing in Grassmannian framework

## 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, $\mathbb{LG}(n, 2n)$, and that they correspond to different ways of fixing the ${\rm GL}(n, \mathbb{C})$ symmetry of $\mathbb{LG}(n, 2n)$. This provides an understanding of the equivalence of these different-looking formulas, and it leads to new twistor-like formulas for 6D superamplitudes.