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We revisit the 3d GLSM computation of the equivariant quantum K-theory ringof the complex Grassmannian from the perspective of line defects. The 3d GLSMonto $X={\rm Gr}(N_c, n_f)$ is a circle compactification of the 3d$\mathcal{N}=2$ supersymmetric gauge theory with gauge group $U(N_c)_{k, k+lN_c}$ and $n_f$ fundamental chiral multiplets, for any choice of theChern-Simons levels $(k,l)$ in the `geometric window'. For$k=N_c-\frac{n_f}{2}$ and $l=-1$, the twisted chiral ring generated by thehalf-BPS lines wrapping the circle has been previously identified with thequantum K-theory ring QK$_T(X)$. We identify new half-BPS line defects in theUV gauge theory, dubbed Grothendieck lines, which flow to the structure sheavesof the (equivariant) Schubert varieties of $X$. They are defined by coupling$\mathcal{N}=2$ supersymmetric gauged quantum mechanics of quiver type to the3d GLSM. We explicitly show that the 1d Witten index of the defect worldlinereproduces the Chern characters for the Schubert classes, which are written interms of double Grothendieck polynomials. This gives us a physical realisationof the Schubert-class basis for QK$_T(X)$. We then use 3d $A$-model techniquesto explicitly compute QK$_T(X)$ as well as other K-theoretic enumerativeinvariants such as the topological metric. We also consider the 2d/0d limit ofour 3d/1d construction, which gives us local defects in the 2d GLSM, theSchubert defects, that realise equivariant quantum cohomology classes.

Grothendieck lines in 3d $\mathcal{N}=2$ SQCD and the quantum K-theory of the Grassmannian