A Comprehensive Survey of Brane Tilings

Abstract

An infinite class of $4d$ $\mathcal{N}=1$ gauge theories can be engineered on the worldvolume of D3-branes probing toric Calabi-Yau 3-folds. This kind of setup has multiple applications, ranging from the gauge/gravity correspondence to local model building in string phenomenology. Brane tilings fully encode the gauge theories on the D3-branes and have substantially simplified their connection to the probed geometries. The purpose of this paper is to push the boundaries of computation and to produce as comprehensive a database of brane tilings as possible. We develop efficient implementations of brane tiling tools particularly suited for this search. We present the first complete classification of toric Calabi-Yau 3-folds with toric diagrams up to area 8 and the corresponding brane tilings. This classification is of interest to both physicists and mathematicians alike.

39 pages. Link to Mathematica modules provided

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Cited by in corpus (14)

• Cluster integrable systems, q-Painleve equations and their quantization
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• Toric geometry and the dual of $c$-extremization
• Cluster Toda chains and Nekrasov functions
• $3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories
• Lectures on the Calabi-Yau Landscape
• On supersymmetry breaking vacua from D-branes at orientifold singularities
• c-extremization from toric geometry
• 5D N=1 super QFT: symplectic quivers
• From N=2 in four dimensions to (0,2) in two dimensions
• Some Open Questions in Quiver Gauge Theory
• Quiver Gauge Theories: Beyond Reflexivity
• Metaheuristic Generation of Brane Tilings
• Genus One Belyi Maps by Quadratic Correspondences