2019/12/09 by Ueda, Kazushi, Yoshida, Yutaka
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1912.03792
We study a correspondence between 3d N=2 topologically twisted Chern-Simons-matter theories on S1 × Σg and quantum K-theory of Grassmannians. Our starting point is a Frobenius algebra depending on a parameter β associated with an algebraic Bethe ansatz introduced by Gorbounov-Korff. They showed that the Frobenius algebra with β=-1 is isomorphic to the (equivariant) small quantum K-ring of the Grassmannian, and the Frobenius algebra with β=0 is isomorphic to the equivariant small quantum cohomology of the Grassmannian. We apply supersymmetric localization formulas to the correlation functions of supersymmetric Wilson loops in the Chern-Simons-matter theory and show that the algebra of Wilson loops is isomorphic to the Frobenius algebra with β=-1. This allows us to identify the algebra of Wilson loops with the quantum K-ring of the Grassmannian. We also show that correlation functions of Wilson loops on S1 × Σg satisfy the axiom of 2d TQFT. For β=0, we show the correspondence between an A-twisted GLSM, the Frobenius algebra for β=0, and the quantum cohomology of the Grassmannian. We also discuss deformations of Verlinde algebras, omega-deformations, and the K-theoretic I-functions of Grassmannians with level structures.