Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence

Abstract

We test the AdS/CFT correspondence by computing the partition function of some $\mathcal{N}=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds $Q^{1,1,1}$ or $V^{5,2}$. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to $N^{3/2}$ and the coefficient matches correctly the volume of $Q^{1,1,1}$ and $V^{5,2}$.

v2. minor revision;v3. clarification on Z extremization, 23 pages, 9 figures

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Cited by in corpus (71)

• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
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• ABJM theory as a Fermi gas
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• N=2 supersymmetric theories on squashed three-sphere
• 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
• Relation between the 4d superconformal index and the S^3 partition function
• Superconformal indices of three-dimensional theories related by mirror symmetry
• The large N limit of quiver matrix models and Sasaki-Einstein manifolds
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Exact results on ABJ theory and the refined topological string
• Three-sphere free energy for classical gauge groups
• The supersymmetric NUTs and bolts of holography
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• N=2 supersymmetric AdS_4 solutions of M-theory
• 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
• The Gravity Dual of Supersymmetric Renyi Entropy
• 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
• Global Supersymmetry on Curved Spaces in Various Dimensions
• Holography of 3d-3d correspondence at Large N
• Entropy functions for accelerating black holes
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories
• Sphere correlation functions and Verma modules
• Free Energy of D_n Quiver Chern-Simons Theories
• Toric Fano varieties and Chern-Simons quivers
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• F-maximization along the RG flows: a proposal
• Refined Checks and Exact Dualities in Three Dimensions
• Aspects of AdS${}_2$ classification in M-theory: Solutions with mesonic and baryonic charges
• 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
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• Localization on round sphere revisited
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• The Hilbert series of U/SU SQCD and Toeplitz Determinants
• On Large N Solution of N=3 Chern-Simons-adjoint Theories
• Comments on F-maximization and R-symmetry in 3D SCFTs
• Z Extremization in Chiral-Like Chern Simons Theories
• Topologically twisted index of $T[SU(N)]$ at large $N$
• On the exact R charge for N=2 CS theories
• Non-toric Cones and Chern-Simons Quivers
• M2-branes and plane partitions
• Solving Mass-deformed Holography Perturbatively
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• A perturbative study of holographic mABJM theory
• 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
• BPS $M2$-branes in $Ad{S}_4\times Q^{1,1,1}$ Dual to Loop Operators
• 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
• Geometric free energy of toric AdS4/CFT3 models
• The AdS/CFT Correspondence and Symmetry Breaking
• Semiclassics of three-dimensional SCFTs from holography