The large N limit of quiver matrix models and Sasaki-Einstein manifolds

Abstract

We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and fixed Chern-Simons levels) of these matrix models for various examples, and show that in this limit the free energy reproduces the expected AdS/CFT result of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding Sasaki-Einstein metric. More generally we conjecture a relation between the large N limit of the partition function, interpreted as a function of trial R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons quivers based on M2 branes at hypersurface singularities, and for a U(N)^3 theory based on M2 branes at a toric singularity.

38 pages, 4 figures; v2: minor changes, typos and factor of 2 in eq. (5.19) fixed, references and 2 figures added; v3: new section 4.5 added; v4: more typos fixed, range of validity of (4.19) clarified

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• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Sasaki-Einstein Manifolds and Volume Minimisation
• Les Houches lectures on matrix models and topological strings
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Brane Tilings and M2 Branes
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• On Large N Solution of Gaiotto-Tomasiello Theory
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Cited by in corpus (66)

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• Summing Up All Genus Free Energy of ABJM Matrix Model
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• Supersymmetry on Curved Spaces and Holography
• Holographic Duals of D=3 N=4 Superconformal Field Theories
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
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• Superconformal indices of three-dimensional theories related by mirror symmetry
• Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
• Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Exact results on ABJ theory and the refined topological string
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• Instanton effects in ABJM theory with general R-charge assignments
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• Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• Instanton Effects in Orbifold ABJM Theory
• D2-brane Chern-Simons theories: F-maximization = a-maximization
• The F-Theorem and F-Maximization
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• Interacting fermions and N=2 Chern-Simons-matter theories
• Holography of 3d-3d correspondence at Large N
• Entropy functions for accelerating black holes
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories
• Free Energy of D_n Quiver Chern-Simons Theories
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Calabi-Yau Volumes and Reflexive Polytopes
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• Refined Checks and Exact Dualities in Three Dimensions
• F-maximization along the RG flows: a proposal
• Exact results for five-dimensional superconformal field theories with gravity duals
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory
• A Systematic Study on Matrix Models for Chern-Simons-matter Theories
• Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Localization on round sphere revisited
• The Hilbert series of U/SU SQCD and Toeplitz Determinants
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Comments on F-maximization and R-symmetry in 3D SCFTs
• On Large N Solution of N=3 Chern-Simons-adjoint Theories
• Z Extremization in Chiral-Like Chern Simons Theories
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Non-toric Cones and Chern-Simons Quivers
• M2-branes and plane partitions
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• A perturbative study of holographic mABJM theory
• Spin(7) duality for N=1 CS-matter theories
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• Klebanov-Witten flows in M-theory
• $\mathcal{I}$-extremization with baryonic charges
• Deconstructing Deformed D-quivers
• Geometric free energy of toric AdS4/CFT3 models
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories
• The Hamilton-Jacobi Equation and Holographic Renormalization Group Flows on Sphere
• Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models
• The AdS/CFT Correspondence and Symmetry Breaking