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Positive configuration space

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arxiv 2003.03904 v3 pith:HDN3VCMV submitted 2020-03-09 math.CO hep-thmath.AG

Nima Arkani-Hamed , Thomas Lam , Marcus Spradlin This is my paper · ORCID
classification math.COhep-thmath.AG
keywords positivespacechowconfigurationnonnegativecellsconesgrassmannian
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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.

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  1. The CEGM NLSM

    hep-th 2025-02 conditional novelty 6.0 of 10

    A systematic deformation theory for CEGM amplitudes yields generalized nonlinear sigma model amplitudes, with dimension gcd(k,n)-1 for pure deformations and an embedding of ordinary NLSM amplitudes as residues.

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