Even-Zohar Chaim, Lakrec Tsviqa, Parisi Matteo, Sherman-Bennett Melissa, Tessler Ran, Williams Lauren
Faculty of Mathematics, Technion, Haifa, Israel.
Institute of Mathematics, University of Zurich, Zürich, Switzerland.
Lett Math Phys. 2024;114(5):111. doi: 10.1007/s11005-024-01854-4. Epub 2024 Sep 11.
The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in super Yang-Mills theory. It generalizes and the 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 amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for . Secondly, we exhibit a tiling of the amplituhedron which involves a tile which does not come from the BCFW recurrence-the 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 . This paper is a companion to our previous paper "Cluster algebras and tilings for the amplituhedron."
放大正多面体是一个数学对象，它被引入以提供超杨 - 米尔斯理论中散射振幅的几何起源。它对[具体内容未提及，原文此处可能有缺失]进行了推广，并且具有与簇代数相关的非常丰富的组合学性质。在本文中，我们给出了一系列关于放大正多面体的平铺和瓷砖的结果。首先，我们根据[具体内容未提及，原文此处可能有缺失]的簇变量对BCFW瓷砖的面进行了完整刻画。其次，我们展示了放大正多面体的一种平铺，其中涉及一个并非来自BCFW递推关系的瓷砖——[具体内容未提及，原文此处可能有缺失]瓷砖，它也满足所有簇性质。最后，通过加强与簇代数的联系，我们表明每个标准BCFW瓷砖都是一个簇簇的正部分，这使我们能够根据[具体内容未提及，原文此处可能有缺失]的簇变量明确计算每个此类瓷砖的典范形式。本文是我们之前论文《放大正多面体的簇代数与平铺》的姊妹篇。
