From weak to strong coupling in ABJM theory

Abstract

The partition function of N=6 supersymmetric Chern-Simons-matter theory (known as ABJM theory) on S^3, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super-matrix model is closely related to a matrix model describing topological Chern-Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS_4 x CP^3 and gives the correct N^{3/2} scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in CP^3. We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi-Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi-Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two 't Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi-Yau, and leads to an expansion around topological Chern-Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.

51 pages, 5 figures; v4: misprints corrected, added constant map contributions to the free energies, which were missing in the previous versions

References in corpus (18)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Fractional M2-branes
• Holographic Wilson Loops
• Open string amplitudes and large order behavior in topological string theory
• Remodeling the B-model
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• Holomorphic anomaly and matrix models
• 1/2-BPS states in M theory and defects in the dual CFTs
• Anomalous radius shift in AdS(4)/CFT(3)
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• 1/2-BPS Wilson Loops and Vortices in ABJM Model
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Topological Strings and (Almost) Modular Forms

Cited by in corpus (290)

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• N=2 supersymmetric theories on squashed three-sphere
• Exact results for the entanglement entropy and the energy radiated by a quark
• Supersymmetric Gauge Theories on the Five-Sphere
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• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• 4d Index to 3d Index and 2d TQFT
• Localization on Hopf surfaces
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Fivebranes and 3-manifold homology
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• The Holography of F-maximization
• Instanton Bound States in ABJM Theory
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Membrane instantons from a semiclassical TBA
• Exact Results on the ABJM Fermi Gas
• Relation between the 4d superconformal index and the S^3 partition function
• Renyi Entropies for Free Field Theories
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory
• Lectures on AdS Black Holes, Holography and Localization
• Perturbative partition function for a squashed S^5
• Holography for $\mathcal{N}=2^{\ast }$ on $S^4$
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• New supersymmetric Wilson loops in ABJ(M) theories
• Exact Slope and Interpolating Functions in ABJM Theory
• Multiple Membranes in M-theory
• A note on perturbation series in supersymmetric gauge theories
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• Probing non-perturbative effects in M-theory
• 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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• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
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• Exact ABJM Partition Function from TBA
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• The large N limit of M2-branes on Lens spaces
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
• Reducing the 4d Index to the S^3 Partition Function
• Resumming the string perturbation series
• Instanton effects in ABJM theory with general R-charge assignments
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Holographic renormalization and supersymmetry
• M-theoretic matrix models
• ABJM Wilson Loops in Arbitrary Representations
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• The Partition Function of ABJ Theory
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
• S^3/Z_n partition function and dualities
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Universal 3d Cardy Block and Black Hole Entropy
• Mass-deformed ABJM and Black Holes in AdS${}_4$
• Extremal Correlators and Random Matrix Theory
• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• Towards the exact Bremsstrahlung function of ABJM theory
• Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity
• AdS${}_7$/CFT${}_6$ with orientifolds
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Hofstadter's Butterfly in Quantum Geometry
• Clustering and the Three-Point Function
• Large $N$ Partition Functions of the ABJM Theory
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• A new AdS_4/CFT_3 Dual with Extended SUSY and a Spectral Flow
• Instanton Effects in Orbifold ABJM Theory
• Strings in AdS_4 x CP^3, Wilson loops in N=6 super Chern-Simons-matter and Bremsstrahlung functions
• On Supersymmetric Gauge Theories on S^4 x S^1
• The F-Theorem and F-Maximization
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• Resurgence of the Cusp Anomalous Dimension
• Interacting fermions and N=2 Chern-Simons-matter theories
• Operators and higher genus mirror curves
• Two-loop cusp anomaly in ABJM at strong coupling
• Holomorphic Anomaly and Quantum Mechanics
• Three-dimensional de Sitter horizon thermodynamics
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Exact Bremsstrahlung functions in ABJM theory
• Resurgence Matches Quantization
• ABJM on ellipsoid and topological strings
• Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
• On exact-WKB analysis, resurgent structure, and quantization conditions
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• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Wilson loops in Five-Dimensional Super-Yang-Mills
• Strong coupling expansion of circular Wilson loops and string theories in AdS${}_5\times {\mathrm{S}}^5$ and AdS${}_4\times {\mathrm{CP}}^3$
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Wilson loops at large $N$ and the quantum M2 brane
• Exact results for perturbative partition functions of theories with SU(2|4) symmetry
• Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories
• Holography of 3d-3d correspondence at Large N
• Instanton Effects in Orientifold ABJM Theory
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• M5-branes and Wilson Surfaces in AdS${}_7$/CFT${}_6$ Correspondence
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• The 1/2 BPS Wilson loop in ABJM theory at two loops
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• Exact relations between M2-brane theories with and without Orientifolds
• Exact probes of orientifolds
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Exact Instanton Expansion of ABJM Partition Function
• Mass Deformations of the ABJM Theory: The Holographic Free Energy
• Exact multi-instantons in topological string theory
• Sphere correlation functions and Verma modules
• Localization at large N in Chern-Simons-matter theories
• Higher derivative effects for 4d AdS gravity
• Large N phase transitions in supersymmetric Chern-Simons theory with massive matter
• Matrix model from N = 2 orbifold partition function
• A profusion of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories
• On the Exact Interpolating Function in ABJ Theory
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Free Energy of D_n Quiver Chern-Simons Theories
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Framing and localization in Chern-Simons theories with matter
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orientifolding of the ABJ Fermi gas
• One-loop corrections to holographic Wilson loop in AdS4xCP3
• $q$-Virasoro modular double and 3d partition functions
• ABJM Theory with mass and FI deformations and Quantum Phase Transitions
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• Chern-Simons theory from M5-branes and calibrated M2-branes
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Airy Function and 4d Quantum Gravity
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• From Schurs to Giants in ABJ(M)
• 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
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory
• The quantum 1/2 BPS Wilson loop in $\mathcal{N}=4$ Chern-Simons-matter theories
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• BPS coherent states and localization
• String theory duals of Wilson loops from Higgsing
• A Systematic Study on Matrix Models for Chern-Simons-matter Theories
• Killing superalgebras for Lorentzian four-manifolds
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• New BPS Wilson loops in $\mathcal{N}\text{= 4}$ circular quiver Chern-Simons-matter theories
• Z-extremization and F-theorem in Chern-Simons matter theories
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Double-Trace Flows and the Swampland
• Mass Deformed ABJM Theory on Three Sphere in Large N limit
• Superfield theories on $S^3$ and their localization
• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• Near-Extremal Black Branes with n*3 Entropy Growth
• Bands and gaps in Nekrasov partition function
• A matrix model for the latitude Wilson loop in ABJM theory
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Localization on round sphere revisited
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• ABJ Wilson loops and Seiberg Duality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Giambelli Identity in Super Chern-Simons Matrix Model
• Toward Precision Holography in Type IIA with Wilson Loops
• ABJ Quadrality
• Spectral Theories and Topological Strings on del Pezzo Geometries
• From the planar limit to M-theory
• Intersecting Defects and Supergroup Gauge Theory
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Hanany-Witten Transition in Quantum Curves
• A Note on Instanton Effects in ABJM Theory
• Z Extremization in Chiral-Like Chern Simons Theories
• Probing Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories at weak coupling
• A note on multiply wound BPS Wilson loops in ABJM
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Matching quantum string corrections and circular Wilson loops in $Ad{S}_4\times C{P}^3$
• Gravity duals of supersymmetric gauge theories on three-manifolds
• Gravity dual of dynamically broken supersymmetry
• Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models
• Exact Holography of the Mass-deformed M2-brane Theory
• What lattice theorists can do for superstring/M-theory
• Thermodynamics of black M-branes from SCFTs
• Localization and Duality for ABJM Latitude Wilson Loops
• Wilson loops on three-manifolds and their M2-brane duals
• Constructing Generalized Self-Dual Strings
• On three-point functions in ABJM and the latitude Wilson loop
• Exact results for ABJ Wilson loops and open-closed duality
• Mass-deformed ABJM Theory and LLM Geometries: Exact Holography
• Localization and Large N reduction on S^3 for the Planar and M-theory limit
• Emergent Phase Space Description of Unitary Matrix Model
• Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
• 1/3 BPS loops and defect CFTs in ABJM theory
• Fermi gas approach to general rank theories and quantum curves
• Killing superalgebras for Lorentzian six-manifolds
• Localization principle in SUSY gauge theories
• Non-toric Cones and Chern-Simons Quivers
• Two-Point Functions in ABJM Matrix Model
• The Phase Diagram of BPS Black Holes in AdS${}_5$
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Multi-cut Solutions in Chern-Simons Matrix Models
• On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 duality
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• Cardy Limits of 6d Superconformal Theories
• SU(N) q-Toda equations from mass deformed ABJM theory
• Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity
• M2-branes and plane partitions
• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
• Classifying BPS bosonic Wilson loops in 3d $\mathcal{N}=4$ Chern-Simons-matter theories
• Airy Equation for the Topological String Partition Function in a Scaling Limit
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• Solving Mass-deformed Holography Perturbatively
• Quantum noncommutative ABJM theory: first steps
• ABJ Theory in the Higher Spin Limit
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
• Vortex loop operators and quantum M2-branes
• Moduli space of supersymmetric QCD in the Veneziano limit
• An exact limit of ABJM
• Brane Transitions from Exceptional Groups
• A perturbative study of holographic mABJM theory
• Gauge and matter superfield theories on $S^2$
• Resolved gravity duals of $\mathcal{N}=4$ quiver field theories in 2+1 dimensions
• Gravitational free energy in topological AdS/CFT
• More Large $N$ limits of 3d gauge theories
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Exact results for Wilson loops in orbifold ABJM theory
• Holographic (Eternal) Inflation
• Duality Cascades and Affine Weyl Groups
• Supersymmetric Wilson loops in two dimensions and duality
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling
• M-Brane Models and Loop Spaces
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA
• Large N instantons from topological strings
• Non-topological Vortex Configurations in the ABJM Model
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• 3d dualities with decoupled sectors and brane transitions
• A new large-N limit and the planar equivalence outside the planar limit
• Duality Cascades and Parallelotopes
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Flavors of entanglement
• On precision holography for the circular Wilson loop in $Ad{S}_5\times S^5$
• Construction of a Massive ABJM Theory Without Higgs Superfields
• $N^2$ entropy of 4D N=4 SYM
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Toward the construction of the general multi-cut solutions in Chern-Simons Matrix Models
• Linear Chern-Simons-matter Theories in the Planar Limit
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• M2- and M5-branes in E11 Current Algebra Formulation of M-theory
• The Hamilton-Jacobi Equation and Holographic Renormalization Group Flows on Sphere
• Dualities from large N orbifold equivalence in Chern-Simons-matter theories with flavor
• The Holographic Contributions to the Sphere Free Energy
• Fermi-gas correlators of ADHM theory and triality symmetry
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories
• M5-branes in AdS${}_4\times Q^{1,1,1}$ spacetime
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories
• Framing fermionic Wilson loops in ABJ(M)
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• On the structure of quadrilateral brane tilings
• Off-shell phase diagram of BPS black holes in AdS${}_5$
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas