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Spinor-Helicity Varieties

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arxiv 2406.17331 v2 pith:BNY4LWGM submitted 2024-06-25 math.AG hep-thmath.CO

Yassine El Maazouz , Anaëlle Pfister , Bernd Sturmfels This is my paper · ORCID
classification math.AGhep-thmath.CO
keywords varietiesspinor-helicityalgebracombinatoricscommutativecomplementarycorrespondencedimension
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The spinor-helicity formalism in particle physics gives rise to natural subvarieties in the product of two Grassmannians. These include two-step flag varieties for subspaces of complementary dimension. Taking Hadamard products leads to Mandelstam varieties. We study these varieties through the lens of combinatorics and commutative algebra, and we explore their tropicalization, positive geometry, and scattering correspondence.

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Cited by 3 Pith papers

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  1. The positive orthogonal Grassmannian

    math.CO 2024-12 conditional novelty 7.0 of 10

    For the positive orthogonal Grassmannian, the authors describe boundaries in the simplest case, prove a duality between two special families, and show the standard cell decomposition fails when n>2k+1.

  2. 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.

  3. Points on Rational Normal Curves and the ABCT Variety

    math.AG 2024-12 conditional novelty 6.0 of 10

    The paper derives a recursive formula for the cohomology class of the ABCT variety V(3,n) inside the Grassmannian G(3,n), using a determinantal realization and Porteous' formula, and matches special coefficients to Eu...

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