Quivers, Tilings, Branes and Rhombi

Abstract

We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact manifold. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.

36 pages, 40 figures, JHEP3

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Cited by in corpus (92)

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• Chiral flavors and M2-branes at toric CY4 singularities
• Crystal Melting and Toric Calabi-Yau Manifolds
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• Characterization of an in-vacuum PILATUS 1M detector
• Brane Tilings and Reflexive Polygons
• Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes
• Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
• Dimer models and cluster categories of Grassmannians
• 2d (0,2) Quiver Gauge Theories and D-Branes
• Cohomological Hall algebras, vertex algebras and instantons
• Dimer models and the special McKay correspondence
• Brane Brick Models and 2d (0,2) Triality
• Quiver Yangian from Crystal Melting
• Quivers, YBE and 3-manifolds
• D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics
• Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
• Brane Tilings and Specular Duality
• Shifted Quiver Yangians and Representations from BPS Crystals
• Charting Class ${\mathcal{S}}_k$ Territory
• Emergent 3-manifolds from 4d Superconformal Indices
• Network and Seiberg Duality
• Chiral theories of class S
• Counting Orbifolds
• New Einstein-Sasaki and Einstein Spaces from Kerr-de Sitter
• Surface defects and elliptic quantum groups
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• On the Classification of Brane Tilings
• Colored BPS Pyramid Partition Functions, Quivers and Cluster Transformations
• New Directions in Bipartite Field Theories
• Higgsing M2-brane Theories
• Toric CFTs, Permutation Triples, and Belyi Pairs
• Symmetries of Abelian Orbifolds
• Higher Cluster Categories and QFT Dualities
• Bipartite Field Theories from D-Branes
• Quiver gauge theories and integrable lattice models
• Calabi-Yau Volumes and Reflexive Polytopes
• Toric Fano varieties and Chern-Simons quivers
• A Comprehensive Survey of Brane Tilings
• Anomalies and O-plane charges in orientifolded brane tilings
• Superconformal index for large N quiver Chern-Simons theories
• Finite $N$ corrections to the superconformal index of orbifold quiver gauge theories
• $3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories
• S-duality in $\mathcal{N}=1$ orientifold SCFTs
• Surface defects as transfer matrices
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• N-ification of Forces: A Holographic Perspective on D-brane Model Building
• Mass-deformed Brane Tilings
• E3-brane instantons and baryonic operators for D3-branes on toric singularities
• Scattering Amplitudes and Toric Geometry
• The Beta Ansatz: A Tale of Two Complex Structures
• Double Handled Brane Tilings
• Branes and instantons intersecting at angles
• Orientifolds of Warped Throats from Toric Calabi-Yau Singularities
• Twin Theories, Polytope Mutations and Quivers for GTPs
• Integrable lattice spin models from supersymmetric dualities
• Toric Lego: A method for modular model building
• Seiberg duality for Chern-Simons quivers and D-brane mutations
• A note on dimer models and McKay quivers
• Brane Geometry and Dimer Models
• An Introduction to Counting Orbifolds
• Gauge origami and quiver W-algebras
• On supersymmetry breaking vacua from D-branes at orientifold singularities
• Branes and integrable lattice models
• Bipartite field theories and D-brane instantons
• Integrability on the Master Space
• Gauge Theories, Tessellations & Riemann Surfaces
• Brane Tilings and Non-Commutative Geometry
• BPS States Meet Generalized Cohomology
• A Note on Dimer Models and D-brane Gauge Theories
• Dimers, Orientifolds and Anomalies
• Toric Quiver Asymptotics and Mahler Measure: $\mathcal{N}=2$ BPS States
• Algorithms for representations of quiver Yangian algebras
• Backreacting D-brane instantons on branes at singularities
• Emerging Non-Anomalous Baryonic Symmetries in the AdS_5/CFT_4 Correspondence
• $\mathcal{N}=1$ conformal dualities from unoriented chiral quivers
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• Deformations of Dimer Models
• Permutation in the CHY-Formulation
• Mahler Measure for a Quiver Symphony
• Some Open Questions in Quiver Gauge Theory
• Holographic Effective Field Theories
• Eulerian digraphs and toric Calabi-Yau varieties
• Klebanov-Witten flows in M-theory
• Dimers in a Bottle
• Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds
• Consistent Dimer Models on Surfaces with Boundary
• 2-simplexes and superconformal central charges
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• Quiver-Invariant Dualities between Brane Tilings
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• On the structure of quadrilateral brane tilings