Abstract
AbstractWe 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.
Funder
National Science Foundation
U.S. Department of Energy
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference54 articles.
1. Ardila, F., Rincón, F., Williams, L.: Positroids and non-crossing partitions. Trans. Am. Math. Soc. 368(1), 337–363 (2016)
2. Arkani-Hamed, N., Bai, Y., Lam, T.: Positive geometries and canonical forms. JHEP 2017, 39 (2017)
3. Arkani-Hamed, N., Bourjaily, J., Cachazo, F., Goncharov, A., Postnikov, A., Trnka, J.: Grassmannian Geometry of Scattering Amplitudes. Cambridge University Press, Cambridge (2016)
4. Arkani-Hamed, N., He, S., Lam, T.: Stringy canonical forms (2019). arXiv:1912.08707
5. Arkani-Hamed, N., He, S., Lam, T.: Cluster configuration spaces of finite type (2020). arXiv:2005.11419
Cited by
30 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献