  The disk partition function of certain 3d N=2 supersymmetric gauge theories
computes a quantum K-theoretic ring for Kahler manifolds X. We study the 3d
gauge theory/quantum K-theory correspondence for global and local Calabi-Yau
manifolds with several Kahler moduli. We propose a multi-cover formula that
relates the 3d BPS world-volume degeneracies computed by quantum K-theory to
Gopakumar-Vafa invariants.
