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

Understand

The $\mathcal{N}=1$ 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.