Positive Configuration Space
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220_2021_Article_4041.pdf
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Author(s)
Arkani-Hamed, Nima
Lam, Thomas
Spradlin, Marcus
Date Issued
April 2021
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Version
Final published version
Abstract
Abstract
We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. Our work is motivated by connections to super Yang–Mills scattering amplitudes, which will be discussed in a sequel.
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/s00220-021-04041-x
