Boundaries of the Amplituhedron with amplituhedronBoundaries

Abstract

Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called ``amplituhedronBoundaries'' for calculating the boundary structures of three positive geometries: the amplituhedron ${\mathcal{A}}_{n,k}^{(m)}$, the momentum amplituhedron ${\mathcal{M}}_{n,k}^{(m)}$ and the hypersimplex ${\Delta }_{k,n}$. The first two geometries are relevant for scattering amplitudes in planar $\mathcal{N}=4$ SYM, while the last one is a well-studied polytope appearing in many contexts in mathematics, and is closely related to ${\mathcal{M}}_{n,k}^{(2)}$. The package includes an array of useful tools for the study of these positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians.

44 pages

References in corpus (2)

• Total positivity, Grassmannians, and networks
• Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica

Cited by in corpus (9)

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• Amplituhedra, and Beyond
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• The Loop Momentum Amplituhedron
• Internal boundaries of the loop amplituhedron
• Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry
• On the geometry of the orthogonal momentum amplituhedron
• The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms
• The Amplituhedron BCFW Triangulation