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

TL;DR

This paper explores N=1 dualities in four-dimensional supersymmetric gauge theories via D-brane configurations in string theory, extending geometric realizations to new models with complex superpotentials.

Contribution

It generalizes geometric realizations of N=1 dualities to models with D_{k+2} superpotentials, including various representations for the fields, broadening the understanding of dualities in string theory.

Findings

Extended geometric realization to new superpotential models.

Analyzed multiple representations for the field Y.

Connected D-brane configurations with gauge theory dualities.

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