Properly ordered dimers,R-charges, and an efficient inverse algorithm

Abstract

The N = 1 superconformal field theories that arise in AdS-CFT from placing a stack of D3-branes at the singularity of a toric Calabi-Yau threefold can be described succinctly by dimer models. We present an efficient algorithm for constructing a dimer model from the geometry of the Calabi-Yau. Since not all dimers produce consistent field theories, we perform several consistency checks on the field theories produced by our algorithm: they have the correct number of gauge groups, their cubic anomalies agree with the Chern-Simons coefficients in the AdS dual, and all gauge invariant chiral operators satisfy the unitarity bound. We also give bounds on the ratio of the central charge of the theory to the area of the toric diagram. To prove these results, we introduce the concept of a properly ordered dimer.

Explicit de Sitter flux vacua for global string models with chiral matter

“…The dimer can be JHEP05(2014)001 obtained from the toric diagram using various inverse algorithms (e.g. [43][44][45]). Numbered faces in the dimer correspond to gauge groups, common nodes of faces to bi-fundamental matter, and the "±" faces correspond to superpotential terms.…”

Brane tilings and reflexive polygons

“…It is of great interest to associate to each worldvolume theory the corresponding mesonic moduli space. For the purpose of a self-contained discussion, a brief review on the forward algorithm [12,77] which translates the gauge theory information into toric data is provided below. Quiver Q.…”

Remarks on quiver gauge theories from open topological string theory

“…Let Z be a weak toric Fano surface, and denote by X = tot(ω Z ) the total space of its canonical bundle. As discussed in [44], there is a consistent brane tiling corresponding to Z (see also [36,71]). Furthermore, the arguments of [45] imply that M θ coincides with X for a particular choice of the GIT parameter θ.…”

“…In order to extract the data of the effective quiver gauge theory from the geometry of Z, several procedures have been developed in [26,27,29,30,36,38], most notably the fast inverse algorithm and the brane tiling method. These have been argued to be equivalent and hence we may restrict our attention to the more elegant latter method.…”