Positive configuration space
Combinatorics
2022-09-01 v3 High Energy Physics - Theory
Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2003.03904,
title = {Positive configuration space},
author = {Nima Arkani-Hamed and Thomas Lam and Marcus Spradlin},
journal= {arXiv preprint arXiv:2003.03904},
year = {2022}
}
Comments
46 pages; v2: citations added; v3: correction (Remark 7.1)