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Wilson loop algebras and quantum K-theory for Grassmannians

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arxiv 1911.13286 v1 pith:SRJRYZN7 submitted 2019-11-29 hep-th math.AG

Wilson loop algebras and quantum K-theory for Grassmannians

Hans Jockers , Peter Mayr , Urmi Ninad , Alexander Tabler This is my paper
classification hep-th math.AG
keywords algebraquantumwilsonalgebrask-theoreticlooprelatedchern-simons
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M,N), isomorphic to the Verlinde algebra for U(M), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

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Cited by 4 Pith papers

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  1. Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials

    hep-th 2026-01 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for partial flag manifolds reproduce parabolic Whitney polynomials for Schubert classes in quantum K-theory and yield new parabolic quantum Grothendieck polynomials.

  2. Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

    hep-th 2025-12 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.

  3. On the Schubert calculus of the quantum K-theory for partial flag manifolds: a 3d A-model perspective

    hep-th 2026-06 unverdicted novelty 6.0

    Computes 2- and 3-point functions of Schubert line defects in 3d A-model for partial flag manifolds Fl(k;n) to obtain K-theoretic Littlewood-Richardson coefficients, with small-beta limit recovering 2d quantum cohomology.

  4. Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries

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    Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.