On the geometry of the orthogonal momentum amplituhedron
| Autor: | Lukowski, Tomasz, Moerman, Robert, Stalknecht, Jonah |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP12(2022)006 |
| Popis: | 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. Comment: 19 pages, 7 figures |
| Databáze: | arXiv |
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