On the geometry of the orthogonal momentum amplituhedron

Abstract

In this paper we study the orthogonal momentum amplituhedron ${\mathcal{O}}_k$, a recently introduced positive geometry that encodes the tree-level scattering amplitudes in ABJM theory. We generate the full boundary stratification of ${\mathcal{O}}_k$ and show that its boundaries can be labelled by so-called orthogonal Grassmannian forests (OG forests). We also determine the generating function for enumerating boundaries according to their dimension and show that the Euler characteristic of ${\mathcal{O}}_k$ 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 studying the positive orthogonal Grassmannian and the orthogonal momentum amplituhedron.

19 pages, 7 figures

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Cited by in corpus (3)

• The two-loop eight-point amplitude in ABJM theory
• Positive Geometry for Stringy Scalar Amplitudes
• The Geometry of BCFW for ABJM Loop Integrands