Peacock patterns and new integer invariants in topological string theory

Abstract

Topological string theory near the conifold point of a Calabi-Yau threefold gives rise to factorially divergent power series which encode the all-genus enumerative information. These series lead to infinite towers of singularities in their Borel plane (also known as "peacock patterns"), and we conjecture that the corresponding Stokes constants are integer invariants of the Calabi-Yau threefold. We calculate these Stokes constants in some toric examples, confirming our conjecture and providing in some cases explicit generating functions for the new integer invariants, in the form of q-series. Our calculations in the toric case rely on the TS/ST correspondence, which promotes the asymptotic series near the conifold point to spectral traces of operators, and makes it easier to identify the Stokes data. The resulting mathematical structure turns out to be very similar to the one of complex Chern-Simons theory. In particular, spectral traces correspond to state integral invariants and factorize in holomorphic/anti-holomorphic blocks.

arXiv comment51 pages, 11 figures, typos corrected, new clarification added

References in corpus (58)

• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Four-dimensional wall-crossing via three-dimensional field theory
• Holomorphic Anomalies in Topological Field Theories
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• Discrete Heisenberg-Weyl Group and Modular Group
• Quantum Dilogarithm
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• ABJM theory as a Fermi gas
• c=1 String as the Topological Theory of the Conifold
• Non-perturbative effects and the refined topological string
• A Primer on Resurgent Transseries and Their Asymptotics
• Quantum Background Independence In String Theory
• Holomorphic Blocks in Three Dimensions
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Factorisation of N = 2 theories on the squashed 3-sphere
• 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
• Fivebranes and 3-manifold homology
• Integrability of the holomorphic anomaly equations
• Instanton Bound States in ABJM Theory
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• 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
• Operators from mirror curves and the quantum dilogarithm
• Matrix models from operators and topological strings
• Topological Strings and Quantum Spectral Problems
• Riemann-Hilbert problems from Donaldson-Thomas theory
• Physical Resurgent Extrapolation
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Resurgence in complex Chern-Simons theory
• Exact quantization conditions for the relativistic Toda lattice
• Exact quantization conditions for cluster integrable systems
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Operators and higher genus mirror curves
• On the Quantum Invariant for the Spherical Seifert Manifold
• Resurgence Matches Quantization
• Chern-Simons theory, analytic continuation and arithmetic
• Exponential Networks and Representations of Quivers
• Quantization condition from exact WKB for difference equations
• Exploring 5d BPS Spectra with Exponential Networks
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• Topological Strings and (Almost) Modular Forms
• The resurgent structure of quantum knot invariants
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II
• Spectral equations for the modular oscillator
• Knots, Perturbative Series and Quantum Modularity
• Resurgence of Chern-Simons theory at the trivial flat connection
• Intrinsic non-perturbative topological strings
• On the spectrum of the local ${\mathbb{P}}^2$ mirror curve

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• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Exact multi-instantons in topological string theory
• On the resurgent structure of quantum periods
• Quantum Curves, Resurgence and Exact WKB
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Black Hole Entropy, Quantum Corrections and EFT Transitions
• Exact instanton transseries for quantum mechanics
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Large N instantons from topological strings
• Resurgence of Refined Topological Strings and Dual Partition Functions
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Resurgence in complex Chern-Simons theory at generic levels
• Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions