Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories

Abstract

We give further support for our conjecture relating eigenvalue distributions of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of operators in the chiral ring of the corresponding supersymmetric three-dimensional gauge theory. We show that the relation holds for non-critical R-charges and for examples with {\mathcal N}=2 instead of {\mathcal N}=3 supersymmetry where the bifundamental matter fields are nonchiral. We prove that, for non-critical R-charges, the conjecture is equivalent to a relation between the free energy of the gauge theory on a three sphere and the volume of a Sasaki manifold that is part of the moduli space of the gauge theory. We also investigate the consequences of our conjecture for chiral theories where the matrix model is not well understood.

27 pages + appendices, 5 figures

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• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• The F-Theorem and F-Maximization
• Monopole Taxonomy in Three-Dimensional Conformal Field Theories
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• Interacting fermions and N=2 Chern-Simons-matter theories
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• On Large N Solution of N=3 Chern-Simons-adjoint Theories
• Z Extremization in Chiral-Like Chern Simons Theories
• Black hole microstates and supersymmetric localization
• Monopole operators, moduli spaces and dualities
• Non-toric Cones and Chern-Simons Quivers
• Integrability on the Master Space
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories
• The braneology of 3D dualities
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories