  For a 3d gauged linear sigma model parametrized by a Kahler manifold X, the
3d BPS index defines a q-series that can be analytically continued in the
Kahler modulus by standard methods. It is argued that an SL(2,Z)-transform of
the Birkhoff connection matrix captures non-perturbative corrections to the 3d
GLSM. As an application, a 3d lift of the standard 2d GLSM for the resolved
conifold is shown to provide a world-volume dual for the non-perturbative
topological string on the resolved conifold. The perturbative 3d BPS index
computes the Gopakumar-Vafa partition function, while the analytic continuation
matches existing proposals for a non-perturbative completion of the topological
string.
