ABJM theory as a Fermi gas

Abstract

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of an ideal Fermi gas with a non-trivial, one-particle quantum Hamiltonian. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the WKB or semiclassical expansion of the quantum gas, and we show that, for several quiver Chern-Simons-matter theories, it is given by an Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas corresponds to a strong coupling expansion in type IIA theory, and it is dual to the genus expansion. This allows us to calculate explicitly non-perturbative effects due to D2-brane instantons in the AdS background.

52 pages, 11 figures. v3: references, corrections and clarifications added, plus a footnote on the relation to the recent work by Hanada et al

References in corpus (14)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Summing Up All Genus Free Energy of ABJM Matrix Model
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• The quantum mechanics of perfect fluids
• Anomalous radius shift in AdS(4)/CFT(3)
• ABJM with Flavors and FQHE
• Massive type IIA string theory cannot be strongly coupled
• Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence
• On Large N Solution of Gaiotto-Tomasiello Theory
• Topological Strings and (Almost) Modular Forms
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory

Cited by in corpus (178)

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• Fivebranes and 3-manifold homology
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• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Instanton Bound States in ABJM Theory
• Membrane instantons from a semiclassical TBA
• Exact Results on the ABJM Fermi Gas
• Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory
• Explicit examples of DIM constraints for network matrix models
• Matrix models from operators and topological strings, 2
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• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• Seiberg-Witten theory as a Fermi gas
• A note on perturbation series in supersymmetric gauge theories
• Operators from mirror curves and the quantum dilogarithm
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• 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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• Higgs branch localization of 3d N=2 theories
• Review of the No-Boundary Wave Function
• Matrix models from operators and topological strings
• Direct derivation of "mirror" ABJ partition function
• The exact Schur index of $\mathcal{N}=4$ SYM
• The large N limit of M2-branes on Lens spaces
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
• Instanton effects in ABJM theory with general R-charge assignments
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Holographic duals of 3d S-fold CFTs
• ABJM Wilson Loops in Arbitrary Representations
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• The M-theory Archipelago
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• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
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• Peacock patterns and new integer invariants in topological string theory
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• Clustering and the Three-Point Function
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• A 2d/1d Holographic Duality
• Operators and higher genus mirror curves
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• Wilson loops at large $N$ and the quantum M2 brane
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• TBA-like integral equations from quantized mirror curves
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• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
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• Twisted M2 brane holography and sphere correlation functions
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
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• A profusion of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories
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• Scale invariance vs conformal invariance
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• Orientifolding of the ABJ Fermi gas
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• $q$-Virasoro modular double and 3d partition functions
• Airy Function and 4d Quantum Gravity
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
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• The $\mathcal{N}=4$ Schur index with Polyakov loops
• 3d mirror symmetry as a canonical transformation
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
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• The quantum 1/2 BPS Wilson loop in $\mathcal{N}=4$ Chern-Simons-matter theories
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• More on holographic correlators: Twisted and dimensionally reduced structures
• Complete factorization in minimal N=4 Chern-Simons-matter theory
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• ABJ Wilson loops and Seiberg Duality
• Divergences and Boundary Modes in N=8 Supergravity
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• From the planar limit to M-theory
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• Probing non-perturbative effects in M-theory on orientifolds
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• Intersecting Defects and Supergroup Gauge Theory
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• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
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• A note on multiply wound BPS Wilson loops in ABJM
• Spectral determinants and quantum theta functions
• Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models
• Conformal bounds in three dimensions from entanglement entropy
• Localization and Large N reduction on S^3 for the Planar and M-theory limit
• Two-Point Functions in ABJM Matrix Model
• Non-toric Cones and Chern-Simons Quivers
• Fermi gas approach to general rank theories and quantum curves
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• The spectral problem of the ABJ Fermi gas
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• Multi-cut Solutions in Chern-Simons Matrix Models
• Quiver indices and Abelianization from Jeffrey-Kirwan residues
• On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 duality
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• The topological open string wavefunction
• Subleading Microstate Counting in the Dual to Massive Type IIA
• Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• 3d superconformal indices and isomorphisms of M2-brane theories
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
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• Vortex loop operators and quantum M2-branes
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• On the Semi-Classical Limit of Scalar Products of the XXZ Spin Chain
• Large N instantons from topological strings
• Exact solutions to quantum spectral curves by topological string theory
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Resumming planar diagrams for the N=6 ABJM cusped Wilson loop in light-cone gauge
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Quantum Periods and TBA-like Equations for a Class of Calabi-Yau Geometries
• Duality Cascades and Parallelotopes
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• A new large-N limit and the planar equivalence outside the planar limit
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Dualities and loops on squashed $S^3$
• Deconstructing Deformed D-quivers
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Quantum curves as quantum distributions
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• Linear Chern-Simons-matter Theories in the Planar Limit
• The Holographic Contributions to the Sphere Free Energy
• Fermi-gas correlators of ADHM theory and triality symmetry
• Topological phase, spin Chern-Simons theory and level rank duality on lens space
• Dualities from large N orbifold equivalence in Chern-Simons-matter theories with flavor
• Inner Product in Quantum Field Theory
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• Notes on Planar Resolvents of Chern-Simons-matter Matrix Models
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas
• Gauge Theories on de Sitter Spacetime
• Application of Quantum Field Theory
• Quantum Mirror Map for Del Pezzo Geometries
• Quantum Field Theory in de Sitter spacetime
• Note on Quantum Periods and a TBA-like System
• Scalar Field Theory on Supermanifolds
• M-Theory on Complex Spacetime