Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-07-18
JHEP 0810:014,2008
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, 19 figures, some corrections and clarifications
Scientific paper
10.1088/1126-6708/2008/10/014
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. To prove these results, we introduce the concept of a properly ordered dimer.
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