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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• $3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories
• Gauge Theories and Dessins d'Enfants: Beyond the Torus
• The Beta Ansatz: A Tale of Two Complex Structures
• Double Handled Brane Tilings
• Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
• Superconformal Block Quivers, Duality Trees and Diophantine Equations
• Gauge Theories, Tessellations & Riemann Surfaces
• Towards the Continuous Limit of Cluster Integrable Systems
• Graph Zeta Function and Gauge Theories
• Dimer algebras, ghor algebras, and cyclic contractions
• Eulerian digraphs and toric Calabi-Yau varieties
• Quiver Gauge Theories: Beyond Reflexivity
• Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function
• Embedding and partial resolution of complex cones over Fano threefolds
• Metaheuristic Generation of Brane Tilings
• Reflexions on Mahler: Dessins, Modularity and Gauge Theories
• Zhegalkin Zebra Motives Digital Recordings of Mirror Symmetry
• Holographic spectral functions for Sasaki-Einstein 5-manifolds
• On the structure of quadrilateral brane tilings