تقرير
A cluster of results on amplituhedron tiles
| العنوان: | A cluster of results on amplituhedron tiles |
|---|---|
| المؤلفون: | Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Tessler, Ran, Sherman-Bennett, Melissa, Williams, Lauren |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, High Energy Physics - Theory, Mathematical Physics, Mathematics - Algebraic Geometry, 05E14, 13F60 |
| الوصف: | The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in $\mathcal{N}=4$ super Yang Mills theory. It generalizes \emph{cyclic polytopes} and the \emph{positive Grassmannian}, and has a very rich combinatorics with connections to cluster algebras. In this article we provide a series of results about tiles and tilings of the $m=4$ amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for $\mbox{Gr}_{4,n}$. Secondly, we exhibit a tiling of the $m=4$ amplituhedron which involves a tile which does not come from the BCFW recurrence -- the \emph{spurion} tile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for $\mbox{Gr}_{4,n}$. This paper is a companion to our previous paper ``Cluster algebras and tilings for the $m=4$ amplituhedron''. Comment: 44 pages, 20 figures. arXiv admin note: text overlap with arXiv:2310.17727 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.15568 |
| رقم الأكسشن: | edsarx.2402.15568 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |