BPS indices, modularity and perturbations in quantum K-theory

A bstract We study a perturbation family of N N = 2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians. The 3d BPS half-index of the gauge theory is connected to the theory of bilateral hypergeometric q -series, and to modular q -characters of a class of conformal field theories in a certain massless limit. Turning on 3d Wilson lines at torsion points leads to mock modular behavior. Perturbed correlators in the IR regime are computed by determining the UV-IR map in the presence of deformations.