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

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 Plücker 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.

37 pages, LaTeX, v2: published version

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