Geometry, D-Branes and N=1 Duality in Four Dimensions II

Abstract

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 $W=Tr{X}^{k+1}+TrX{Y}^2$. 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.

15 pages, latex

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