2020年8月

# 3d $$\mathcal{N}$$ = 2 Chern-Simons-matter theory, Bethe ansatz, and quantum K -theory of Grassmannians

Journal of High Energy Physics
• Kazushi Ueda
• ,
• Yutaka Yoshida

2020
8

DOI
10.1007/jhep08(2020)157

Springer Science and Business Media LLC

<title>A<sc>bstract</sc>
</title>We study a correspondence between 3d <inline-formula><alternatives><tex-math>$$\mathcal{N}$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math></alternatives></inline-formula> = 2 topologically twisted Chern-Simons-matter theories on <italic>S</italic>1<italic>×</italic> Σ<italic>g</italic> and quantum <italic>K</italic> -theory of Grassmannians. Our starting point is a Frobenius algebra depending on a parameter <italic>β</italic> associated with an algebraic Bethe ansatz introduced by Gorbounov-Korff. They showed that the Frobenius algebra with <italic>β</italic> = <italic>−</italic>1 is isomorphic to the (equivariant) small quantum <italic>K</italic> -ring of the Grassmannian, and the Frobenius algebra with <italic>β</italic> = 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 <italic>β</italic> = <italic>−</italic>1. This allows us to identify the algebra of Wilson loops with the quantum <italic>K</italic> - ring of the Grassmannian. We also show that correlation functions of Wilson loops on <italic>S</italic>1<italic>×</italic> Σ<italic>g</italic> satisfy the axiom of 2d TQFT. For <italic>β</italic> = 0, we show the correspondence between an A-twisted GLSM, the Frobenius algebra for <italic>β</italic> = 0, and the quantum cohomology of the Grassmannian. We also discuss deformations of Verlinde algebras, omega-deformations, and the <italic>K</italic> -theoretic <italic>I</italic> -functions of Grassmannians with level structures.

リンク情報
DOI
https://doi.org/10.1007/jhep08(2020)157
arXiv
http://arxiv.org/abs/arXiv:1912.03792
URL