Instanton Effects in ABJM Theory from Fermi Gas Approach

Abstract

We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.

42 pages, 26 eps figures; v2: references added

References in corpus (5)

• 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
• Exact ABJM Partition Function from TBA

Cited by in corpus (100)

• Non-perturbative effects and the refined topological string
• Instanton Bound States in ABJM Theory
• Membrane instantons from a semiclassical TBA
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Seiberg-Witten theory as a Fermi gas
• Probing non-perturbative effects in M-theory
• Operators from mirror curves and the quantum dilogarithm
• Exact results on ABJ theory and the refined topological string
• Solving M-theory with the Conformal Bootstrap
• Matrix models from operators and topological strings
• Direct derivation of "mirror" ABJ partition function
• ABJ Fractional Brane from ABJM Wilson Loop
• Topological Strings and Quantum Spectral Problems
• Resumming the string perturbation series
• Instanton effects in ABJM theory with general R-charge assignments
• M-theoretic matrix models
• ABJM Wilson Loops in Arbitrary Representations
• Exact quantization conditions for the relativistic Toda lattice
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact quantization conditions for cluster integrable systems
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Peacock patterns and new integer invariants in topological string theory
• Hofstadter's Butterfly in Quantum Geometry
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Large $N$ Partition Functions of the ABJM Theory
• Instanton Effects in Orbifold ABJM Theory
• Operators and higher genus mirror curves
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• Resurgence Matches Quantization
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Exact WKB methods in $SU(2)$ $N_f=1$
• Quantization condition from exact WKB for difference equations
• Blowup Equations for Refined Topological Strings
• Instanton Effects in Orientifold ABJM Theory
• TBA-like integral equations from quantized mirror curves
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Exact Instanton Expansion of ABJM Partition Function
• Exact eigenfunctions and the open topological string
• Localization at large N in Chern-Simons-matter theories
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orientifolding of the ABJ Fermi gas
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• Wilson loops in unitary matrix models at finite $N$
• Calabi-Yau geometry and electrons on 2d lattices
• Exponential Networks, WKB and Topological String
• Airy Function and 4d Quantum Gravity
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• 3d mirror symmetry as a canonical transformation
• BPS relations from spectral problems and blowup equations
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• A Systematic Study on Matrix Models for Chern-Simons-matter Theories
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Giambelli Identity in Super Chern-Simons Matrix Model
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Probing non-perturbative effects in M-theory on orientifolds
• A Note on Instanton Effects in ABJM Theory
• Hanany-Witten Transition in Quantum Curves
• Functional Equations and Separation of Variables for Exact g-Function
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Spectral determinants and quantum theta functions
• Exact results for ABJ Wilson loops and open-closed duality
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Fermi gas approach to general rank theories and quantum curves
• Two-Point Functions in ABJM Matrix Model
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• SU(N) q-Toda equations from mass deformed ABJM theory
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Geometric transition in Non-perturbative Topological string
• On the spectrum of the local ${\mathbb{P}}^2$ mirror curve
• Microscopics of de Sitter Entropy from Precision Holography
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
• Exact results for Wilson loops in orbifold ABJM theory
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Duality Cascades and Affine Weyl Groups
• Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling
• Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• Duality Cascades and Parallelotopes
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle
• Mellin-Barnes Representation of the Topological String
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas
• Note on Quantum Periods and a TBA-like System
• Painlevé Kernels and Surface Defects at Strong Coupling