Grassmannian Geometry of Scattering Amplitudes

By N. Arkani-Hamed, J. Bourjaily, F. Cachazo, A. Goncharov, Alexander Postnikov, J. Trnka. 2016

459 citations recorded by the source corpus.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7c57a7f228bd5114c91f68d9f0998ab166fe43a3

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In Geometry and Topology

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Citations in the corpus

The twist for positroid varieties (2016, methodology): “Bridge decompositions were introduced in [2]; we will use [17] as our reference for their properties.”
Cluster algebras (2014, unknown): “Building on [3], Arkani-Hamed and Trnka [7] introduced the (tree) amplituhedron, which is the image of the positive Grassmannian under a positive linear map.”
Positive geometries and canonical forms (2017, methodology): “Our methods are not able to rigorously prove it, but a triangulation of this Grassmann polytope appears to be given by the images under Z of the four 4-dimensional positroid cells [2][3][4][5] : (∗1) = 0, [1][2][3][5] : (∗4) = 0, [1][2][3][4] : (∗5) = 0, [12][34][5] : (12) = (34) = 0 (7.”
The EFT-hedron (2020, background): “It is striking to see “all minors of a matrix positive" conditions–earlier seen in the context of the positive grassmannian [4] and the amplituhedron [5] for N = 4 SYM, show up again in a different setting, and in such a basic way, for completely general theories.”
TASI Lectures on Scattering Amplitudes (2017, background): “On-shell tools have excavated a landscape of structures: hidden Yangian and dual conformal symmetries [80, 81, 82, 83, 84], reformulations of the S-matrix in twistor space [85, 86, 22, 87, 88, 89, 90, 91] and Grassmannian space [92, 93, 94], as well as connections to abstract volumes [12, 95] like t”
Regularity theorem for totally nonnegative flag varieties (2019, background): “Totally positive spaces have attracted a lot of interest due to their appearances in other contexts such as cluster algebras [9] and the physics of scattering amplitudes [1].”