BCFW tilings and cluster adjacency for the amplituhedron

• 成果类型: Article
• 署名作者: Even-Zohar, Chaim; Lakrec, Tsviqa; Parisi, Matteo; Sherman-Bennett, Melissa; Tessler, Ran; Williams, Lauren
• 署名单位: Technion Israel Institute of Technology; University of Geneva; Harvard University; Institute for Advanced Study - USA; Massachusetts Institute of Technology (MIT); Weizmann Institute of Science; Harvard University
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-9133
• DOI: 10.1073/pnas.2408572122
• 发表日期: 2024-03-25

摘要

In 2005, Britto, Cachazo, Feng, and Witten gave a recurrence (now known as the BCFW recurrence) for computing scattering amplitudes in N = 4 super Yang-Mills theory. Arkani-Hamed and Trnka subsequently introduced the amplituhedron to give a geometric interpretation of the BCFW recurrence. Arkani-Hamed and Trnka conjectured that each way of iterating the BCFW recurrence gives a triangulation or tiling of the m=4 amplituhedron. In this article, we prove the BCFW tiling conjecture of Arkani-Hamed and Trnka. We also prove the cluster adjacency conjecture for BCFW tiles of the amplituhedron, which says that facets of tiles are cut out by collections of compatible cluster variables for the Grassmannian Gr4,n. Moreover we show that each BCFW tile is the subset of the Grassmannian where certain cluster variables have particular signs.