Non-perturbative effects and the refined topological string

Abstract

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

38 pages, 5 figures

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• The Refined Topological Vertex
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Extended Holomorphic Anomaly in Gauge Theory
• Exact ABJM Partition Function from TBA
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Large D-instanton effects in string theory
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Topological Strings and (Almost) Modular Forms
• The refined BPS index from stable pair invariants

Cited by in corpus (140)

• Refined stable pair invariants for E-, M- and [p,q]-strings
• Matrix models from operators and topological strings, 2
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Seiberg-Witten theory as a Fermi gas
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• 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
• Solving M-theory with the Conformal Bootstrap
• Matrix models from operators and topological strings
• Direct derivation of "mirror" ABJ partition function
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• 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
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Exact quantization conditions for the relativistic Toda lattice
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• 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
• Instanton Effects in Orbifold ABJM Theory
• Instanton effects and quantum spectral curves
• Operators and higher genus mirror curves
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Blowup Equations for 6d SCFTs. I
• Non-Perturbative Quantum Geometry III
• The $\mathcal{N}=2$ Schur index from free fermions
• Resurgence Matches Quantization
• ABJM on ellipsoid and topological strings
• On exact-WKB analysis, resurgent structure, and quantization conditions
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Finite N from Resurgent Large N
• Blowup Equations for Refined Topological Strings
• A Solvable Deformation of Quantum Mechanics
• Quantization condition from exact WKB for difference equations
• Exact WKB Analysis of N = 2 Gauge Theories
• Instanton Effects in Orientifold ABJM Theory
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• TBA-like integral equations from quantized mirror curves
• Exact relations between M2-brane theories with and without Orientifolds
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Exact Instanton Expansion of ABJM Partition Function
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Non-Perturbative Quantum Geometry
• Exact eigenfunctions and the open topological string
• Localization at large N in Chern-Simons-matter theories
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• Orientifolding of the ABJ Fermi gas
• Wilson loops in unitary matrix models at finite $N$
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Calabi-Yau geometry and electrons on 2d lattices
• Exponential Networks, WKB and Topological String
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• Airy Function and 4d Quantum Gravity
• Quantum Curves, Resurgence and Exact WKB
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• BPS relations from spectral problems and blowup equations
• 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
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
• ABJ Wilson loops and Seiberg Duality
• ABJ Quadrality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Probing non-perturbative effects in M-theory on orientifolds
• Intersecting Defects and Supergroup Gauge Theory
• Giambelli Identity in Super Chern-Simons Matrix Model
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM
• Hanany-Witten Transition in Quantum Curves
• Functional Equations and Separation of Variables for Exact g-Function
• A Note on Instanton Effects in ABJM Theory
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Spectral determinants and quantum theta functions
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Exact results for ABJ Wilson loops and open-closed duality
• Pure N=2 Super Yang-Mills and Exact WKB
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• The spectral problem of the ABJ Fermi gas
• Two-Point Functions in ABJM Matrix Model
• Multi-cut Solutions in Chern-Simons Matrix Models
• SU(N) q-Toda equations from mass deformed ABJM theory
• Towards U(N|M) knot invariant from ABJM theory
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• Chern-Simons theory with the exceptional gauge group as a refined topological string
• ABJ Theory in the Higher Spin Limit
• Topological String Geometry
• 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
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Brane Transitions from Exceptional Groups
• On the spectrum of the local ${\mathbb{P}}^2$ mirror curve
• Geometric transition in Non-perturbative Topological string
• A Hyperkähler geometry associated to the BPS structure of the resolved conifold
• Resummations and Non-Perturbative Corrections
• Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling
• Duality Cascades and Affine Weyl Groups
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Exact Chern-Simons / Topological String duality
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Exact solutions to quantum spectral curves by topological string theory
• Quantum mirror curve of periodic chain geometry
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Quantum Periods and TBA-like Equations for a Class of Calabi-Yau Geometries
• Duality Cascades and Parallelotopes
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• On refined Chern-Simons / topological string duality for classical gauge groups
• Notes on Planar Resolvents of Chern-Simons-matter Matrix Models
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas
• On partition functions of refined Chern-Simons theories on $S^3$
• Quantum Mirror Map for Del Pezzo Geometries
• Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves
• Painlevé Kernels and Surface Defects at Strong Coupling
• Note on Quantum Periods and a TBA-like System