Grothendieck lines in 3d SQCD and Quantum K-theory of the Grassmannian

Abstract

In this talk I will revisit the correspondence between 3d $\mathcal{N}=2$ SQCD and the quantum K-theory of the Grassmannian variety Gr$(N_c, n_f)$. 3d $N=2$ SQCD has gauge group $U(N_c)_{k,k+l N_c}$ and $n_f$ chiral matter multiplets in the fundamental representation of $U(N_c)$. By analysing the moduli space of 3d vacua, we will fix the values of the Chern-Simons (CS) levels $(k,l)$ that give us 3d GLSMs that flow to 3d NLSMs with target Gr$(N_c,n_f)$. Then, I will review the 3d A-model of these GLSMs and the relation between the correlation functions in this model and quantum K-theory ring of the Grassmannian. A standard basis of this ring is given by the Schubert classes. These are the classes of the structure sheaves of the Schubert subvarieties. I will show how one can construct line operators in the 3d GLSM that flow to these classes in the IR. This talk is based on [arXiv: 2301.10753, 2305.00534, 2309.06980] with C. Closset.