A cluster of results on amplituhedron tiles
Name
11005_2024_Article_1854.pdf
Size
1.42 MB
Format
Adobe PDF
Checksum (MD5)
b2e5418c9810cb9be067c32617a42023
Author(s)
Even-Zohar, Chaim
Lakrec, Tsviqa
Parisi, Matteo
Sherman-Bennett, Melissa
Tessler, Ran
Williams, Lauren
Date Issued
September 11, 2024
Journal
Letters in Mathematical Physics
Publisher
Springer Netherlands
Citation
Letters in Mathematical Physics. 2024 Sep 11;114(5):111
Version
Final published version
Abstract
The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in =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 Gr4,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 canonica
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s11005-024-01854-4
