Open string amplitudes and large order behavior in topological string theory

Abstract

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi-Yau manifolds. We find closed expressions for various open string amplitudes beyond the disk, and in particular we write down the annulus amplitude in terms of theta functions on a Riemann surface. We test these ideas on local curves and local surfaces, providing in this way generating functionals for open Gromov-Witten invariants in the spirit of mirror symmetry. In the case of local curves, we study the open string sector near the critical point which leads to 2d gravity, and we show that toric D-branes become FZZT branes in a double-scaling limit. We use this connection to compute non-perturbative instanton effects due to D-branes that control the large order behavior of topological string theory on these backgrounds

40 pages, 5 figures, v3: further clarifications and references added

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Cited by in corpus (126)

• From weak to strong coupling in ABJM theory
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• A Primer on Resurgent Transseries and Their Asymptotics
• JT gravity as a matrix integral
• Exact Results in ABJM Theory from Topological Strings
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• Torus knots and mirror symmetry
• Direct Integration of the Topological String
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• A & B model approaches to surface operators and Toda theories
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Integrability of the holomorphic anomaly equations
• Holomorphic anomaly and matrix models
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• A-polynomial, B-model, and Quantization
• Algebraic methods in random matrices and enumerative geometry
• The D5-brane effective action and superpotential in N=1 compactifications
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• A holomorphic and background independent partition function for matrix models and topological strings
• Matrix models from operators and topological strings
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Seiberg-Witten theory and matrix models
• The uses of the refined matrix model recursion
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Intersection numbers of spectral curves
• Local Mirror Symmetry for One-Legged Topological Vertex
• Think globally, compute locally
• Virasoro constraints for Kontsevich-Hurwitz partition function
• Orbifold Hurwitz numbers and Eynard-Orantin invariants
• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• ABJM Wilson loops in the Fermi gas approach
• Reconstructing WKB from topological recursion
• The spectral curve of the Eynard-Orantin recursion via the Laplace transform
• Hurwitz numbers, matrix models and enumerative geometry
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Resurgence Matches Quantization
• A generalized topological recursion for arbitrary ramification
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• Gromov-Witten invariants of $\bp^1$ and Eynard-Orantin invariants
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Finite N from Resurgent Large N
• Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String
• Topological open strings on orbifolds
• Evidence for Tadpole Cancellation in the Topological String
• Large N duality beyond the genus expansion
• Black Holes and Large Order Quantum Geometry
• Open topological strings and integrable hierarchies: Remodeling the A-model
• A short overview of the "Topological recursion"
• Exact results for topological strings on resolved Y(p,q) singularities
• Exact multi-instantons in topological string theory
• Exact eigenfunctions and the open topological string
• On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
• The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers
• Local Mirror Symmetry for the Topological Vertex
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• The Volume Conjecture and Topological Strings
• Resonant resurgent asymptotics from quantum field theory
• BPS relations from spectral problems and blowup equations
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry
• Quantum curves and conformal field theory
• Lectures on Knot Homology and Quantum Curves
• Nonlinear PDEs for Fredholm determinants arising from string equations
• Invariants of spectral curves and intersection theory of moduli spaces of complex curves
• JT gravity and the asymptotic Weil-Petersson volume
• Quantum Mirror Curves for ${\mathbb{C}}^3$ and the Resolved Confiold
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Universality of the topological string at large radius and NS-brane resurgence
• Spectral determinants and quantum theta functions
• Integrality structures in topological strings I: framed unknot
• Open String Invariants and Mirror Curve of the Resolved Conifold
• The remodeling conjecture and the Faber-Pandharipande formula
• D-Branes in Topological String Theory
• D-instanton, threshold corrections, and topological string
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• A matrix model for the topological string II: The spectral curve and mirror geometry
• ABCD of Beta Ensembles and Topological Strings
• The topological open string wavefunction
• Towards U(N|M) knot invariant from ABJM theory
• Supereigenvalue Models and Topological Recursion
• Topological Recursion in The Ramond Sector
• Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a Point
• Solving the Topological String on K3 Fibrations
• Quantizing Weierstrass
• Mirror of the refined topological vertex from a matrix model
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• On a proof of the Bouchard-Sulkowski conjecture
• Matrix models for topological strings: exact results in the planar limit
• Reconstructing GKZ via topological recursion
• A Lagrangean formalism for Hermitean matrix models
• On explicit formulae of LMOV invariants
• Topological strings, quiver varieties and Rogers-Ramanujan identities
• Large N instantons from topological strings
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• $\mathcal{N}=1$ Super Topological Recursion
• Resurgence of Refined Topological Strings and Dual Partition Functions
• Torus Knots in Lens Spaces & Topological Strings
• Exact solutions to quantum spectral curves by topological string theory
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• $q$-Difference Kac-Schwarz Operators in Topological String Theory
• Some comments on the local curve (B-side)
• On equivariant mirror symmetry for local P^2
• Symplectic cuts and open/closed strings I
• A Unitary Matrix Model for $q$-deformed Plancherel Growth
• Enumerative geometry of surfaces and topological strings
• Equivariant Gromov-Witten Theory of Affine Smooth Toric Deligne-Mumford Stacks
• Geometric Transition as a Change of Polarization
• Painlevé Kernels and Surface Defects at Strong Coupling
• The Laplace transform, mirror symmetry, and the topological recursion of Eynard-Orantin