Unhiggsing the del Pezzo

TL;DR

This paper introduces an unhiggsing method to derive gauge theories for blowups of geometries, specifically applying it to del Pezzo surfaces, advancing understanding of non-toric cases and supporting duality concepts.

Contribution

It presents a novel unhiggsing procedure for constructing gauge theories of blowup geometries, including non-toric del Pezzo surfaces, and explores implications for duality and superpotential derivation.

Findings

Unhiggsed gauge theories for cone over third del Pezzo surface.

Introduction of pseudo del Pezzos as non-toric examples.

Support for toric duality and superpotential derivation methods.

Abstract

We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for blowups of geometries whose gauge theory data are known. As specific applications we unhiggs the well-studied theories for the cone over the third del Pezzo surface. We arrive at what we call pseudo del Pezzos and these will constitute a first step toward the understanding of higher, non toric del Pezzos. Moreover, our methods and results give further support for toric duality as well as obtaining superpotentials from global symmetry considerations.