Dimers and Orientifolds

TL;DR

This work develops a comprehensive, dimer-based framework to construct and classify orientifolds of toric Calabi–Yau 3-fold singularities and to derive the resulting D3-brane gauge theories. By treating orientifolds as $ ext{Z}_2$ actions on brane tilings, the authors derive explicit projection rules, global sign parities, and geometric actions on mesons, and they connect these to both the direct IIB picture and the mirror geometry. The approach unifies known orientifolded theories, yields numerous new examples including non-orbifold cases, and extends to line-orientifolds; it also provides practical tools for analyzing tadpole cancellation, anomaly constraints, and potential non-perturbative effects such as D-brane instantons. The framework enables systematic model-building with applications to dynamical SUSY breaking and non-perturbative superpotential terms, and it offers a productive bridge to HW configurations and their T-duals, enriching both phenomenology and mathematical structure of toric orientifolds.

Abstract

We introduce new techniques based on brane tilings to investigate D3-branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge theories living on the D-branes. Using the set of ideas in this paper one recovers essentially all orientifolded theories known so far. Furthermore, new orientifolds of non-orbifold toric singularities are obtained. The possible applications of the tools presented in this paper are diverse. One particular application is the construction of models which feature dynamical supersymmetry breaking as well as the computation of D-instanton induced superpotential terms.

Figures (41)

• Figure 1: The two basic examples of possible reflections as applied to the dimer of the conifold: a) A point reflection. b) A line reflection. The dotted box marks the unit cell of the periodic tiling and defines the $\mathbb T^2$ of the dimer. The red crosses mark the fixed points under the point reflection in the $\mathbb T^2$, while the red lines mark the fixed lines under the line reflection. Under point reflections white nodes are exchanged with black nodes, indicating arrow (orientation) reversal in the quiver.
• Figure 2: Left: The dimer of $\mathbb C^3$ and the four fixed points under the point reflection. Right: The three fundamental mesons (edges crossed by the blue lines) assocciated to coordinates of $\mathbb C^3$.
• Figure 3: Left: The fundamental cell of Figure 1 for the conifold with fixed-points of the orientifold action. Right: The mesonic operators.
• Figure 4: Left: $\mathbb C^2/\mathbb Z_2 \times \mathbb C$ dimer with fixed-points. Center and right: The mesonic operators. We show two equivalent representations $w$ and $w"$ of the same meson, and an intermediate path $w'$.
• Figure 5: Left: $\mathbb C^2/\mathbb Z_2 \times \mathbb C$ dimer with fixed-points for a different orientifold action. Right: The mesonic operators.