Gauge Theories from Toric Geometry and Brane Tilings

Abstract

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds L^{a,b,c} is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L^{a,b,a}, whose smallest member is the Suspended Pinch Point.

46 pages, 21 figures, JHEP3. v2: minor changes and references added. v3: typos and two figures corrected

References in corpus (60)

• Gauge Theory Correlators from Non-Critical String Theory
• The Holographic Weyl anomaly
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• The Exact Superconformal R-Symmetry Maximizes a
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Branes, Superpotentials and Superconformal Fixed Points
• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Supersymmetric AdS_5 solutions of M-theory
• The 2004 UTfit Collaboration Report on the Status of the Unitarity Triangle in the Standard Model
• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Dimer models and toric diagrams
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• Toric Sasaki-Einstein metrics on S^2 x S^3
• New Type IIB Vacua and their F-Theory Interpretation
• Phase Structure of D-brane Gauge Theories and Toric Duality
• From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
• Symmetries of Toric Duality
• New checks and subtleties for AdS/CFT and a-maximization
• The dual superconformal theory for Lpqr manifolds
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• Fractional Branes and Dynamical Supersymmetry Breaking
• Evidence for the Strongest Version of the 4d a-Theorem, via a-Maximization Along RG Flows
• Supersymmetry Breaking from a Calabi-Yau Singularity
• Brane Configurations for Branes at Conifolds
• Baryon Spectra and AdS/CFT Correspondence
• Supersymmetry breaking at the end of a cascade of Seiberg dualities
• Sasaki-Einstein Metrics on S^2 x S^3
• Cascading RG Flows from New Sasaki-Einstein Manifolds
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Chaotic Duality in String Theory
• Quiver Theories from D6-branes via Mirror Symmetry
• Dibaryons from Exceptional Collections
• Generalized Conifolds and 4d N=1 SCFT
• RG Fixed Points and Flows in SQCD with Adjoints
• The Toric Phases of the Y^{p,q} Quivers
• A New Infinite Class of Quiver Gauge Theories
• New Results on the "$a$-theorem" in Four Dimensional Supersymmetric Field Theory
• Conformal Manifolds for the Conifold and other Toric Field Theories
• Multi-Flux Warped Throats and Cascading Gauge Theories
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• Marginal Deformations of Field Theories with AdS_4 Duals
• Dibaryon Spectroscopy
• Marginal Deformations with U(1)^3 Global Symmetry
• N=1 RG Flows, Product Groups, and a-Maximization
• Branes at Generalized Conifolds and Toric Geometry
• Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals
• Holographic dual of the Standard Model on the throat
• Towards Supergravity Duals of Chiral Symmetry Breaking in Sasaki-Einstein Cascading Quiver Theories
• A Family of N=1 SU(N)^k Theories from Branes at Singularities
• A Mixed Phase of SUSY Gauge Theories from a-Maximization
• A new Ricci flat geometry
• Geodesic flows and contact toric manifolds
• Undoing Orbifold Quivers
• Symplectic toric orbifolds

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