Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

Abstract

We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.

35 pages, 20 figures; reference added. The simulation code is available upon request to [email protected]

References in corpus (21)

• 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
• Notes on SUSY Gauge Theories on Three-Sphere
• ABJM theory as a Fermi gas
• Summing Up All Genus Free Energy of ABJM Matrix Model
• N=2 supersymmetric theories on squashed three-sphere
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Anomalous radius shift in AdS(4)/CFT(3)
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• N=4 Super Yang-Mills from the Plane Wave Matrix Model
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• A Note on the Partition Function of ABJM theory on S^3
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• Non-planar ABJM Theory and Integrability
• On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 duality
• Supersymmetry non-renormalization theorem from a computer and the AdS/CFT correspondence
• Generating new dualities through the orbifold equivalence: a demonstration in ABJM and four-dimensional quivers
• A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory

Cited by in corpus (82)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• ABJM theory as a Fermi gas
• Non-perturbative effects and the refined topological string
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• Instanton Bound States in ABJM Theory
• Membrane instantons from a semiclassical TBA
• Exact Results on the ABJM Fermi Gas
• Matrix models from operators and topological strings, 2
• Operators from mirror curves and the quantum dilogarithm
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Higgs branch localization of 3d N=2 theories
• Matrix models from operators and topological strings
• Direct derivation of "mirror" ABJ partition function
• ABJ Fractional Brane from ABJM Wilson Loop
• Instanton effects in ABJM theory with general R-charge assignments
• Resumming the string perturbation series
• ABJM Wilson Loops in Arbitrary Representations
• The Partition Function of ABJ Theory
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• ABJM Wilson loops in the Fermi gas approach
• Instanton Effects in Orbifold ABJM Theory
• Large $N$ Partition Functions of the ABJM Theory
• Instanton effects and quantum spectral curves
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Exact relations between M2-brane theories with and without Orientifolds
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Exact Instanton Expansion of ABJM Partition Function
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Localization at large N in Chern-Simons-matter theories
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Orientifolding of the ABJ Fermi gas
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• From Schurs to Giants in ABJ(M)
• On Perturbation theory improved by Strong coupling expansion
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Non-topological logarithmic corrections in minimal gauged supergravity
• From the planar limit to M-theory
• Probing non-perturbative effects in M-theory on orientifolds
• ABJ Quadrality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models
• Thermodynamics of black M-branes from SCFTs
• Localization and Large N reduction on S^3 for the Planar and M-theory limit
• Exact results for ABJ Wilson loops and open-closed duality
• Two-Point Functions in ABJM Matrix Model
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 duality
• The topological open string wavefunction
• The origin of space-time as seen from matrix model simulations
• Statistical Physics of the Polarised IKKT Matrix Model
• 3d superconformal indices and isomorphisms of M2-brane theories
• Markov Chain Monte Carlo for Dummies
• A One-Loop Test of Quantum Supergravity
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory
• Resummations and Non-Perturbative Corrections
• Exact results for Wilson loops in orbifold ABJM theory
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling
• 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
• Exact solutions to quantum spectral curves by topological string theory
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• M2- and M5-branes in E11 Current Algebra Formulation of M-theory
• Dualities from large N orbifold equivalence in Chern-Simons-matter theories with flavor
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas