Phase Structure of D-brane Gauge Theories and Toric Duality

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Abstract
Harnessing the unimodular degree of freedom in the definition of any toric diagram, we present a method of constructing inequivalent gauge theories which are world-volume theories of D-branes probing the same toric singularity. These theories are various phases in partial resolution of Abelian orbifolds. As examples, two phases are constructed for both the zeroth Hirzebruch and the second del Pezzo surfaces. We show that such a phenomenon is a special case of ``Toric Duality'' proposed in hep-th/0003085. Furthermore, we investigate the general conditions that distinguish these different gauge theories with the same (toric) moduli space.

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