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, the momentum amplituhedron and the hypersimplex. The first two geometries are relevant for scattering amplitudes in planar N=4 supersymmetric Yang–Mills theory, while the last one is a well-studied polytope appearing in many contexts in mathematics, and is closely related to the m=2 momentum amplituhedron. 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. Program summary: Program title: amplituhedronBoundaries CPC Library link to program files: http://dx.doi.org/10.17632/fhcnzn3z96.1 Developer's repository link: https://github.com/mrmrob003/amplituhedronBoundaries Licensing provisions: GNU General Public License 3 Programming language: Wolfram MATHEMATICA 11.0 Nature of problem: The package facilitates the determination and study of the boundary stratifications for three positive geometries: the amplituhedron, the momentum amplituhedron, and the hypersimplex. The first two geometries are relevant for scattering amplitudes in planar N=4 sYM, while the last one is a well-studied polytope appearing in many important contexts in mathematics. Solution method: The package includes an array of useful tools for exploring the three aforementioned positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians. Restrictions: Wolfram MATHEMATICA 11.0 or above