Geometry, D-branes and N = 1 duality in four dimensions. II

We study N = 1 dualities in four dimensional supersymmetric gauge theories in terms of wrapping D 6-branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. We generalize the recent work of geometrical realization for the models which have the superpotential corresponding to an A_k type singularity, to various models presented by Brodie and Strassler, consisting of D_k+2 superpotential of the form W = TrX^k+1 + TrXY². We discuss a large number of representations for the field Y, but with X always in the adjoint (symmetric) [antisymmetric] representation for SU(SO)[Sp] gauge groups.