Unhiggsing the del Pezzo

TL;DR

<3-5 sentence high-level summary>The paper develops an unhiggsing framework to construct D-brane worldvolume gauge theories for blowups of known singularities, and applies it to the cone over the third del Pezzo surface to generate toric but non-generic (pseudo) del Pezzos, designated PdP4 and PdP5. Through explicit quivers, superpotentials, and symmetry analyses, the authors show toric duality coincides with Seiberg duality and validate their results using forward/inverse toric algorithms. The work reveals that unhiggsing yields a controllable, scalable path to new gauge theories beyond toric cases, though the resulting moduli spaces correspond to non-generic blowups with non-isolated singularities. These pseudo-del Pezzos provide a valuable step toward understanding higher del Pezzos and their gauge theories, with implications for broader geometric engineering and duality structures.

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.