D-Brane Gauge Theories from Toric Singularities and Toric Duality

TL;DR

This paper introduces an algorithm to derive gauge theories from toric singularities, illustrating the method with examples and discussing the phenomenon of different theories sharing the same moduli space, termed 'Toric Duality.'

Contribution

It provides a systematic algorithm for extracting gauge theory data from toric varieties and explores the concept of Toric Duality, revealing multiple theories with identical moduli spaces.

Findings

Algorithm for gauge theory extraction from toric data

Examples of gauge theories on del Pezzo and Hirzebruch surfaces

Identification of Toric Duality with different theories sharing the same moduli space

Abstract

Via partial resolution of Abelian orbifolds we present an algorithm for extracting a consistent set of gauge theory data for an arbitrary toric variety whose singularity a D-brane probes. As illustrative examples, we tabulate the matter content and superpotential for a D-brane living on the toric del Pezzo surfaces as well as the zeroth Hirzebruch surface. Moreover, we discuss the non-uniqueness of the general problem and present examples of vastly different theories whose moduli spaces are described by the same toric data. Our methods provide new tools for calculating gauge theories which flow to the same universality class in the IR. We shall call it ``Toric Duality.''