dc.contributor.author | Lukowski, Tomasz | |
dc.contributor.author | Parisi, Matteo | |
dc.contributor.author | Williams, Lauren K. | |
dc.date.accessioned | 2023-03-29T14:30:02Z | |
dc.date.available | 2023-03-29T14:30:02Z | |
dc.date.issued | 2023-10-01 | |
dc.identifier.citation | Lukowski , T , Parisi , M & Williams , L K 2023 , ' The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron ' , International Mathematical Research Notices , vol. 2023 , no. 19 , rnad010 , pp. 16778-16836 . https://doi.org/10.1093/imrn/rnad010 | |
dc.identifier.issn | 1073-7928 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/2002.06164v4 | |
dc.identifier.other | ORCID: /0000-0002-4159-3573/work/132083900 | |
dc.identifier.uri | http://hdl.handle.net/2299/26141 | |
dc.description | © The Author(s) 2023. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. | |
dc.description.abstract | The positive Grassmannian [FIGURE] is a cell complex consisting of all points in the real Grassmannian whose Plücker coordinates are non-negative. In this paper we consider the image of the positive Grassmannian and its positroid cells under two different maps: the moment map μ onto the hypersimplex [31] and the amplituhedron map ˜Z onto the amplituhedron [6]. For either map, we define a positroid dissection to be a collection of images of positroid cells that are disjoint and cover a dense subset of the image. Positroid dissections of the hypersimplex are of interest because they include many matroid subdivisions; meanwhile, positroid dissections of the amplituhedron can be used to calculate the amplituhedron’s ‘volume’, which in turn computes scattering amplitudes in N = 4 super Yang-Mills. We define a map we call T-duality from cells of [FIGURE] to cells of [FIGURE] and conjecture that it induces a bijection from positroid dissections of the hypersimplex k +1, n to positroid dissections of the amplituhedron A n k ,2; we prove this conjecture for the (infinite) class of BCFW dissections. We note that T-duality is particularly striking because the hypersimplex is an (n − 1)-dimensional polytope while the amplituhedron A n k ,2 is a 2k-dimensional non-polytopal subset of the Grassmannian Gr k k +2. Moreover, we prove that the positive tropical Grassmannian is the secondary fan for the regular positroid subdivisions of the hypersimplex, and prove that a matroid polytope is a positroid polytope if and only if all 2D faces are positroid polytopes. Finally, toward the goal of generalizing T-duality for higher m, we define the momentum amplituhedron for any even m. | en |
dc.format.extent | 59 | |
dc.format.extent | 1081394 | |
dc.language.iso | eng | |
dc.relation.ispartof | International Mathematical Research Notices | |
dc.title | The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron | en |
dc.contributor.institution | Mathematics and Theoretical Physics | |
dc.contributor.institution | School of Physics, Engineering & Computer Science | |
dc.contributor.institution | Department of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=85175148973&partnerID=8YFLogxK | |
rioxxterms.versionofrecord | 10.1093/imrn/rnad010 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |