On the Classification of Brane Tilings

Abstract

We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most comprehensive study of such objects to date.

33 pages, 12 figures, 15 tables

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• Brane Tilings
• Tilings, Chern-Simons Theories and M2 Branes
• Brane Tilings and M2 Branes
• Brane Tilings and Their Applications
• Towards M2-brane Theories for Generic Toric Singularities
• Properly ordered dimers, $R$-charges, and an efficient inverse algorithm
• Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories
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