ADE superpotentials, Seiberg Duality and Matrix Models

In this thesis we study some issues of the nonperturbative dynamics of N=1 supersymmetric gauge theories. we consider SQCD with two chiral superfields in the adjoint representation and superpotential deformations, whose flows fall into Arnold's ADE classification of simple singularities. We study in detail the confining phase deformation of the An SQCD and its Seiberg dual in the classical and quantum chiral ring and find the duality map by means of the DV method. Then we analyze the deformation of the Dn+2 SQCD and describe its three classical branches and its cubic curve. In all the cases we can continuously interpolate between the classical vacua by follopwing a path in the moduli space. We are led to the proposal that, for an N=1 supersymmetric gauge theory with a mass gap, the degree of its algebraIc curve corresponds to the number of semiclassical branches.