Open associahedra and scattering forms

TL;DR

This paper advances the understanding of open associahedra in bi-color scattering amplitudes by exploring their facet geometries and introducing new recursion methods for their canonical forms.

Contribution

It uncovers new geometric phenomena like fiber-product structures and generalizes recursion relations to unbounded polytopes for open associahedra.

Findings

Discovered fiber-product geometries in open associahedra

Developed recursion procedures for unbounded polytopes

Extended geometric understanding of scattering amplitudes

Abstract

We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in arXiv:1912.08307. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product geometries. We then provide novel recursion procedures for calculating the canonical form of open associahedra, generalizing recursion relations for bounded polytopes to unbounded polytopes.