The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

Abstract

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.

30 pages, 5 figures

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Seiberg Duality in Chern-Simons Theory
• Comments on 3d Seiberg-like dualities
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Cited by in corpus (32)

• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• Exact results on ABJ theory and the refined topological string
• Three-sphere free energy for classical gauge groups
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Instanton Effects in Orbifold ABJM Theory
• The F-Theorem and F-Maximization
• Instanton Effects in Orientifold ABJM Theory
• Folding Orthosymplectic Quivers
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Free Energy of D_n Quiver Chern-Simons Theories
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• 3d mirror symmetry as a canonical transformation
• A Systematic Study on Matrix Models for Chern-Simons-matter Theories
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• ABJ Quadrality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Non-toric Cones and Chern-Simons Quivers
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• Charges of Monopole Operators in $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories
• Linear Chern-Simons-matter Theories in the Planar Limit
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Superconformal Index for $\mathcal{N}=3$ $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories