Dimers in a bottle

Abstract

We revisit D3-branes at toric CY3 singularities with orientifolds and their description in terms of dimer models. We classify orientifold actions on the dimer through smooth involutions of the torus. In particular, we describe new orientifold projections related to maps on the dimer without fixed points, leading to Klein bottles. These new orientifolds lead to novel $$ \mathcal{N} $$ N = 1 SCFT’s that resemble, in many aspects, non-orientifolded theories. For instance, we recover the presence of fractional branes and some of them trigger a cascading RG-flow à la Klebanov-Strassler. The remaining involutions lead to non-supersymmetric setups, thus exhausting the possible orientifolds on dimers.

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

“…Note that when the toric diagram is a rectangle, such a projection cannot be obtained either with fixed points or with fixed lines, which implies that in order to include the last step of the chain the orientifold projection must be realized differently on the five-brane diagram. As we will see in the next section, this occurs for a chain of L a,b,a /Z 2 models with a particular orientifold projection introduced in [55] known as glide orientifold. This will play an important role in the remainder.…”

“…Another difference with the construction presented in [38,39] is that here we will observe that in some cases fractional branes will not be required. Observe also that in these L a,b,a /Z 2 models the type IIA description is not readily available and the orientifold projection can be performed on the dimer model with the techniques of [27] and the recent extension of [55] in terms of a Klein bottle. This is the other main novelty of the construction performed here.…”

“…In this section we are going to introduce the class of orientifold models L a,b,a /Z 2 , which we will focus on hereafter. In the first subsection we discuss the glide orientifold projection introduced in [55], which we will perform in the case a = b. The second subsection is devoted to a description of the models involved and the results.…”

“…This is interesting, as the five-brane diagram and the brane tiling are embedded in a torus and the orientifold projection is realized as a Z 2 involution. While the past literature mostly focuses on projections with fixed loci, the case of a glide orientifold was recently analyzed in [55]. This involution maps a point to another by combining a shift by half a period of the fundamental cell with a reflection about one of its axes, see figure 15b.…”

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

“…This is interesting, as the five-brane diagram and the brane tiling are embedded in a torus and the orientifold projection is realized as a Z 2 involution. While the past literature mostly focuses on projections with fixed loci, the case of a glide orientifold was recently analyzed in [55]. This involution maps a point to another by combining a shift by half a period of the fundamental cell with a reflection about one of its axes, see Fig.…”