Wilson loop algebras and quantum K-theory for Grassmannians
Hans Jockers, Peter Mayr, Urmi Ninad, Alexander Tabler
TL;DR
This paper explores the algebraic structure of Wilson line operators in 3D supersymmetric gauge theories and their relation to quantum K-theory and Gromov-Witten invariants for Grassmannians, revealing connections to various algebraic rings.
Contribution
It establishes a link between Wilson loop algebras in supersymmetric gauge theories and quantum K-theoretic invariants of Grassmannians, unifying different algebraic structures.
Findings
Wilson loop algebra matches quantum cohomology for certain levels
Algebra realizes Verlinde algebra at specific Chern-Simons levels
Connections to quantum K-theory of Grassmannians are demonstrated
Abstract
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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