Wilson loop algebras and quantum K-theory for Grassmannians

Abstract

Abstract We study the algebra of Wilson line operators in three-dimensional N $$ \mathcal{N} $$ = 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.

Keywords

• Chern-Simons Theories
• Supersymmetric Gauge Theory
• Wilson
• ’t Hooft and Polyakov loops