Summing Up All Genus Free Energy of ABJM Matrix Model

Abstract

The localization technique allows us to compute the free energy of the U(N)_k x U(N)_{-k} Chern-Simons-matter theory dual to type IIA strings on AdS_4 x CP^3 from weak to strong 't Hooft coupling λ= N / k at finite N, as demonstrated by Drukker, Marino, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up all the 1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form -- the Airy function, Ai (k^{4/3} λ_r), with the renormalized 't Hooft coupling λ_r.

18 pages, no figures, v2: typos corrected and references added

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• Fractional M2-branes
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• Holomorphic anomaly and matrix models
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Cited by in corpus (39)

• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• 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
• Review of the No-Boundary Wave Function
• Sphere partition functions and cut-off AdS
• M-theoretic matrix models
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Instanton Effects in Orbifold ABJM Theory
• Large $N$ Partition Functions of the ABJM Theory
• Euclidean Supergravity
• Wilson loops at large $N$ and the quantum M2 brane
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• ABJ Wilson loops and Seiberg Duality
• ABJ Quadrality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• M2-branes and plane partitions
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Vortex loop operators and quantum M2-branes
• Microscopics of de Sitter Entropy from Precision Holography
• Spin Structures and AdS${}_4$ Holography
• Duality Cascades and Affine Weyl Groups
• A new large-N limit and the planar equivalence outside the planar limit
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Duality Cascades and Parallelotopes
• Dualities and loops on squashed $S^3$
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview