Phase structure and critical processes of spectral curves in large N dualities

We examine the phase structure and the critical processes of the spectral curves that arise in the study of large N dualities between supersymmetric Yang-Mills theories and string models on local Calabi-Yau manifolds. These spectral curves are determined by a set of complex partial 't Hooft parameters and a system of cuts given by projections on the spectral curve of minimal supersymmetric cycles of the underlying Calabi-Yau manifold. Using a combination of analytical and numerical methods we give a complete description of the one-cut phase in the cubic model, determine the analytic condition satisfied by critical one-cut spectral curves, and give an algorithm to calculate the two-cut spectral curves of the cubic model for generic values of the partial 't Hooft parameters.