  We describe the magnetic phase of SU(N) $\mathcal{N}=2$ Super Yang-Mills
theories in the self-dual Omega background in terms of a new class of multi-cut
matrix models. These arise from a non-perturbative completion of topological
strings in the dual four dimensional limit which engineers the gauge theory in
the strongly coupled magnetic frame. The corresponding spectral determinants
provide natural candidates for the tau functions of isomonodromy problems for
flat spectral connections associated to the Seiberg-Witten geometry.
