Positive configuration space

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.

46 pages; v2: citations added; v3: correction (Remark 7.1)

References in corpus (2)

• Scattering Equations: From Projective Spaces to Tropical Grassmannians
• Positive configuration space

Cited by in corpus (17)

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• Truncated cluster algebras and Feynman integrals with algebraic letters
• Positive configuration space
• Schubert Problems, Positivity and Symbol Letters
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• Planar Matrices and Arrays of Feynman Diagrams: Poles for Higher $k$
• Generalized permutahedra and positive flag Dressians
• Generalized Color Orderings: CEGM Integrands and Decoupling Identities
• Critical varieties in the Grassmannian
• The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms
• The tropical symplectic Grassmannian
• Polyhedral and Tropical Geometry of Flag Positroids
• Extended DBI and its generalizations from graded soft theorems