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arXiv · 2112.03294

On the geometry of the orthogonal momentum amplituhedron

Tomasz Lukowski·Robert Moerman·Jonah Stalknecht
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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.

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Tomasz Lukowski, Robert Moerman, Jonah Stalknecht. 2021-12-06. On the geometry of the orthogonal momentum amplituhedron. https://doi.org/10.1007/jhep12(2022)006

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