ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras

Abstract

A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply-laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the $F$-polynomials of the corresponding cluster algebras. In addition, we show that the toric variety associated to the g-vector fan has the property that its nef cone is simplicial.

26 pages. v2: added co-author, added section on nef cone of the g-vector fan, other minor changes

References in corpus (5)

• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Cluster Configuration Spaces of Finite Type
• Polytopal realizations of finite type $\mathbf{g}$-vector fans
• Tropical $F$-polynomials and General Presentations
• Positivity and canonical bases in rank 2 cluster algebras of finite and affine types

Cited by in corpus (4)

• Celebrating Loday's Associahedron
• BCFW like recursion for Deformed Associahedron
• Denseness of $g$-vector cones from weighted orbifolds
• A continuous associahedron of type A