From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization

Abstract

AdS/CFT predicts a precise relation between the central charge a, the scaling dimensions of some operators in the CFT on D3-branes at conical singularities and the volumes of the horizon and of certain cycles in the supergravity dual. We review how a quantitative check of this relation can be performed for all toric singularities. In addition to the results presented in hep-th/0506232, we also discuss the relation with the recently discovered map between toric singularities and tilings; in particular, we discuss how to find the precise distribution of R-charges in the quiver gauge theory using dimers technology.

arXiv comment13 pages, 4 figures; proceedings of the RTN workshop: ``Constituents, Fundamental Forces and Symmetries of the Universe'', Corfu, Greece, 20-26 Sept. 2005

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• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Gauge Theories from Toric Geometry and Brane Tilings
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Supersymmetric AdS_5 solutions of M-theory
• Einstein manifolds and conformal field theories
• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Dimer models and toric diagrams
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• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• Toric Sasaki-Einstein metrics on S^2 x S^3
• From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
• New checks and subtleties for AdS/CFT and a-maximization
• The dual superconformal theory for Lpqr manifolds
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Sasaki-Einstein Metrics on S^2 x S^3
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Quiver Theories from D6-branes via Mirror Symmetry
• Five-dimensional Supergravity Dual of a-Maximization
• Current Correlators and AdS/CFT Geometry
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Cited by in corpus (39)

• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Tilings, Chern-Simons Theories and M2 Branes
• The Master Space of N=1 Gauge Theories
• Brane Tilings and M2 Branes
• Brane Tilings and Their Applications
• Machine Learning of Calabi-Yau Volumes
• Counting Chiral Operators in Quiver Gauge Theories
• Brane Tilings and Reflexive Polygons
• A geometric dual of $c$-extremization
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
• Brane Tilings and Exceptional Collections
• Comments on the non-conformal gauge theories dual to Ypq manifolds
• Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
• Deformations of conformal theories and non-toric quiver gauge theories
• Deformations of Toric Singularities and Fractional Branes
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• Comments on Anomalies and Charges of Toric-Quiver Duals
• Exactly marginal deformations of quiver gauge theories as seen from brane tilings
• Calabi-Yau Volumes and Reflexive Polytopes
• Finite $N$ corrections to the superconformal index of toric quiver gauge theories
• Double Handled Brane Tilings
• New Example of Infinite Family of Quiver Gauge Theories
• Quiver Gauge Theory and Conformality at the TeV Scale
• A note on dimer models and McKay quivers
• Master Space and Hilbert Series for N=1 Field Theories
• Monopole operators, moduli spaces and dualities
• Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds
• Free Yang-Mills vs. Toric Sasaki-Einstein
• 5D N=1 super QFT: symplectic quivers
• Dimers, Orientifolds and Anomalies
• c-extremization from toric geometry
• Equivalence of A-Maximization and Volume Minimization
• Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory
• Triangle Anomalies from Einstein Manifolds
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Geometric free energy of toric AdS4/CFT3 models
• Hilbert Series of Bipartite Field Theories
• Quiver-Invariant Dualities between Brane Tilings