Multi-planarizable quivers, orientifolds, and conformal dualities

We study orientifold projections of families of four-dimensional 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 β-deformation of N = 4 SYM. Our construction generalizes previous results on the orientifold projections of the PdP3b and PdP3c singularities.