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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

Hans Jockers , Peter Mayr , Urmi Ninad , Alexander Tabler This is my paper · ORCID
classification hep-thmath.AG
keywords algebraquantumwilsonalgebrask-theoreticlooprelatedchern-simons
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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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  1. Quantum K-theory levels in physics and math

    hep-th 2025-06 conditional novelty 6.0 of 10

    Chern-Simons levels and Ruan-Zhang levels are identified as the same twisting of quantum K-theory, with Coulomb branch equations matching difference operator symbols and geometric windows matching mirror triviality.

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