Explicit factorization of Seiberg-Witten curves with matter from random matrix models

Within the Dijkgraaf-Vafa correspondence, we study the complete factorization of the Seiberg-Witten curve for U(N_c) gauge theory with N_f<N_c massive flavors. We obtain explicit expressions, from random matrix theory, for the moduli, parametrizing the curve. These moduli characterize the submanifold of the Coulomb branch where all monopoles become massless. We find that the matrix model reveals some non-trivial structures of the gauge theory. In particular the moduli are additive with respect to adding extra matter and increasing the number of colors.