On the geometry of the orthogonal momentum amplituhedron

Abstract

Abstract In this paper we focus on the orthogonal momentum amplituhedron $$ \mathcal{O} $$ O k, a recently introduced positive geometry that encodes the tree-level scattering amplitudes in ABJM theory. We generate the full boundary stratification of $$ \mathcal{O} $$ O k for various k and conjecture that its boundaries can be labelled by so-called orthogonal Grassmannian forests (OG forests). We determine the generating function for enumerating these forests according to their dimension and show that the Euler characteristic of the poset of these forests equals one. This provides a strong indication that the orthogonal momentum amplituhedron is homeomorphic to a ball. This paper is supplemented with the Mathematica package orthitroids which contains useful functions for exploring the structure of the positive orthogonal Grassmannian and the orthogonal momentum amplituhedron.