$\mathcal{N}=1$ conformal dualities from unoriented chiral quivers

TL;DR

This paper explores orientifold projections of 4d $ =1$ toric gauge theories, revealing new dualities and conformal connections, including a novel glide orientifold without fixed loci, and demonstrates their flow to the same conformal manifold.

Contribution

It introduces a new class of orientifold projections, including glide orientifolds, and shows these theories are connected by exactly marginal deformations, expanding understanding of dualities in chiral quiver theories.

Findings

Different orientifold projections lead to theories with identical central charges and anomalies.

Some projections are realized via glide orientifolds without fixed loci.

The theories flow to the same conformal manifold connected by quadratic marginal deformations.

Abstract

We study various orientifold projections of 4d $\mathcal{N}=1$ toric gauge theories, associated with CY singularities known as $L^{a,b,a}/\mathbb{Z}_2$, with $a+b$ even. We obtain superconformal chiral theories that have the same central charge, anomalies and superconformal index, whereas they were different before the orientifold. Some of these projections are implemented by a novel type of orientifold without fixed loci, known as glide orientifold. We claim that these theories flow to the same conformal manifold, and they are connected by quadratic exactly marginal deformations. The latter can be written in terms of conjugate pairs of bifundamental fields of $R$-charge one, generalizing previous results for unoriented non-chiral theories.