  We study a perturbation family of 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.
