Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D

TL;DR

This paper develops a new algebraic approach using 6D Grassmannian formulas and dual conformal symmetry to compute 4-point scattering amplitudes, providing explicit solutions and advancing understanding of amplitude structures.

Contribution

It introduces a novel algebra-based method leveraging 6D dual conformal symmetry to derive Grassmannian formulas for scattering amplitudes, including explicit 4-point solutions.

Findings

Derived algebraic equations for amplitude integrands

Explicit 4-point amplitude solutions obtained

Utilized symmetry arguments to constrain formulas

Abstract

We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D $\mathcal{N}=4$ SYM, and therefore we consider a 6D Grassmannian formula, where we can take advantage of massless kinematics. We next use symmetry arguments, and in particular, 6D dual conformal symmetry generalized to arbitrary dual conformal weights. Assuming a rational ansatz in terms of Pl\"{u}cker coordinates (i.e. minors) for the integrand, this approach leads to a set of algebraic equations. As an example, we explicitly find the solution for 4-point scattering amplitudes up to proportionality constants.