Phase Structure of D-brane Gauge Theories and Toric Duality

TL;DR

This paper develops a method to construct different gauge theories associated with the same toric singularity, revealing a form of duality among D-brane world-volume theories and analyzing their distinguishing features.

Contribution

It introduces a systematic approach to generate inequivalent gauge theories from a single toric diagram, expanding understanding of toric duality and phase structure in D-brane gauge theories.

Findings

Constructed multiple phases for Hirzebruch and del Pezzo surfaces.

Demonstrated that these phases are special cases of toric duality.

Identified conditions distinguishing different gauge theories with identical moduli spaces.

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.