From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))

Abstract

The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with {\cal N}=3 supersymmetry and U(N)^d gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S^3. The conjectured F-theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S^3.

3 figures, 41 pages; v2 minor improvements, refs added

References in corpus (13)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• Notes on SUSY Gauge Theories on Three-Sphere
• Sasaki-Einstein Manifolds and Volume Minimisation
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• 3d Partition Function as Overlap of Wavefunctions
• Refined test of AdS4/CFT3 correspondence for N=2,3 theories
• Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
• AdS/CFT with Tri-Sasakian Manifolds
• Z-extremization and F-theorem in Chern-Simons matter theories

Cited by in corpus (57)

• On the RG running of the entanglement entropy of a circle
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
• Exact results on ABJ theory and the refined topological string
• Three-sphere free energy for classical gauge groups
• Direct derivation of "mirror" ABJ partition function
• Instanton effects in ABJM theory with general R-charge assignments
• Holographic duals of 3d S-fold CFTs
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Aspects of Defects in 3d-3d Correspondence
• Instanton Effects in Orbifold ABJM Theory
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• The F-Theorem and F-Maximization
• Complete Intersection Moduli Spaces in N=4 Gauge Theories in Three Dimensions
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• Interacting fermions and N=2 Chern-Simons-matter theories
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Holographic RG flows on curved manifolds and the $F$-theorem
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Exact Instanton Expansion of ABJM Partition Function
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• Supersymmetric Indices of 3d S-fold SCFTs
• Sphere correlation functions and Verma modules
• Localization at large N in Chern-Simons-matter theories
• Free Energy of D_n Quiver Chern-Simons Theories
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• 3d Mirror Symmetry from S-duality
• Rethinking mirror symmetry as a local duality on fields
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Variations on S-fold CFTs
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Z Extremization in Chiral-Like Chern Simons Theories
• On Large N Solution of N=3 Chern-Simons-adjoint Theories
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Monopole operators, moduli spaces and dualities
• Non-toric Cones and Chern-Simons Quivers
• Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Masses, Sheets and Rigid SCFTs
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• On ${\mathrm{SQED}}_3$ and ${\mathrm{SQCD}}_3$: phase transitions and integrability
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview