Tropical fans, scattering equations and amplitudes

Understand

We describe a family of tropical fans related to Grassmannian cluster algebras.

• These fans are related to the kinematic space of massless scattering processes in a number of ways.
• For each fan associated to the Grassmannian ${\rm Gr}(k,n)$ there is a notion of a generalised $\phi^3$ amplitude and an associated set of scattering equations which further generalise the ${\rm Gr}(k,n)$ scattering equations that have been recently introduced.
• Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations.