Multi-planarizable quivers, orientifolds, and conformal dualities

TL;DR

This paper explores orientifold projections of 4D $ abla=1$ toric quiver gauge theories, revealing multiple inequivalent models connected by conformal dualities through marginal deformations like sign flips in superpotentials.

Contribution

It introduces a new class of orientifold projections for quivers with multiple periodic diagrams, establishing conformal dualities via marginal deformations.

Findings

Identifies multiple inequivalent models from a single quiver family.

Shows conformal duality via sign-flip deformations in superpotentials.

Generalizes previous orientifold projection results.

Abstract

We study orientifold projections of families of four-dimensional $\mathcal{N}=1$ toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise, in general, to inequivalent models. A suitable orientifold projection relates a subfamily of the latter by conformal duality. That is, there exist exactly marginal deformations that connect the projected models. The deformations take the form of a sign flip in some of the superpotential interactions, similarly to the $\beta$-deformation of $\mathcal{N}=4$ SYM. Our construction generalizes previous results on the orientifold projections of the PdP$_{3b}$ and PdP$_{3c}$ singularities.