Chaim Even-Zohar, Tsviqa Lakrec, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Lauren Williams
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引用次数: 0
Abstract
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 cyclic polytopes and the 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 \(\text{ Gr}_{4,n}\). Secondly, we exhibit a tiling of the \(m=4\) amplituhedron which involves a tile which does not come from the BCFW recurrence—the 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 \(\text{ Gr}_{4,n}\). This paper is a companion to our previous paper “Cluster algebras and tilings for the \(m=4\) amplituhedron.”
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.