Counting Chiral Operators in Quiver Gauge Theories

Abstract

We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number of D-branes. Explicit formulae are given for few examples, including C^3/Z_3, F_0, and dP_1.

75 pages, 22 figures

References in corpus (62)

• An Index for 4 dimensional Super Conformal Theories
• D-branes, Quivers, and ALE Instantons
• 4d Conformal Field Theories and Strings on Orbifolds
• Branes Intersecting at Angles
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Counting chiral primaries in N=1 d=4 superconformal field theories
• On Conformal Theories in Four Dimensions
• D-Branes And Mirror Symmetry
• Gauge Theories from Toric Geometry and Brane Tilings
• Giant Gravitons in Conformal Field Theory
• Large branes in AdS and their field theory dual
• Orbifold Resolution by D-Branes
• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• Brane Dimers and Quiver Gauge Theories
• Counting Gauge Invariants: the Plethystic Program
• Dimer models and toric diagrams
• A Geometric Unification of Dualities
• Baryons and Domain Walls in an N = 1 Superconformal Gauge Theory
• Aspects of Type IIB Theory on ALE Spaces
• Phase Structure of D-brane Gauge Theories and Toric Duality
• From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
• Symmetries of Toric Duality
• Giant Gravitons from Holomorphic Surfaces
• The dual superconformal theory for Lpqr manifolds
• Quivers, Tilings, Branes and Rhombi
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Supersymmetric states of N=4 Yang-Mills from giant gravitons
• D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
• On the realization of chiral four-dimensional gauge theories using branes
• Baryon Spectra and AdS/CFT Correspondence
• Counting BPS operators in N=4 SYM
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Brane Boxes and Branes on Singularities
• Quiver Theories from D6-branes via Mirror Symmetry
• Dibaryons, Branes, And Strings In AdS Orbifold Models
• BPS Branes From Baryons
• Counting 1/8-BPS Dual-Giants
• N=4 Superconformal Characters and Partition Functions
• Dual Giant Gravitons in Sasaki-Einstein Backgrounds
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Gauge Theories at Resolved and Deformed Singularities using Dimers
• Index for Orbifold Quiver Gauge Theories
• From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
• Brane Tilings and Exceptional Collections
• Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
• Toric AdS4/CFT3 duals and M-theory Crystals
• Dibaryon Spectroscopy
• Comments on the non-conformal gauge theories dual to Ypq manifolds
• Deformations of conformal theories and non-toric quiver gauge theories
• Deformations of Toric Singularities and Fractional Branes
• Comments on Anomalies and Charges of Toric-Quiver Duals
• A Combinatorial Study on Quiver Varieties
• Dual giant gravitons in AdS${}_m$ $\times$ Y${}^n$ (Sasaki-Einstein)
• Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
• Exactly marginal deformations of quiver gauge theories as seen from brane tilings
• Global symmetries and 't Hooft anomalies in brane tilings
• Finite Theories and Marginal Operators on the Brane
• BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators
• New Example of Infinite Family of Quiver Gauge Theories
• Finite N Index and Angular Momentum Bound from Gravity
• Zonotopes and four-dimensional superconformal field theories
• Plethystics and instantons on ALE spaces

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• Quivers as Calculators: Counting, Correlators and Riemann Surfaces
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• M2-brane Probe Dynamics and Toric Duality
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• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• E3-brane instantons and baryonic operators for D3-branes on toric singularities
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• Typicality, Black Hole Microstates and Superconformal Field Theories
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• Master Space and Hilbert Series for N=1 Field Theories
• Gauge Theory RG Flows from a Warped Resolved Orbifold
• Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
• Hilbert Series and Moduli Spaces of k U(N) Vortices
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
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• Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
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• Holographic spectral functions for Sasaki-Einstein 5-manifolds
• Semiclassics of three-dimensional SCFTs from holography