Operators and higher genus mirror curves

Abstract

We perform further tests of the correspondence between spectral theory and topological strings, focusing on mirror curves of genus greater than one with nontrivial mass parameters. In particular, we analyze the geometry relevant to the SU(3) relativistic Toda lattice, and the resolved C^3/Z_6 orbifold. Furthermore, we give evidence that the correspondence holds for arbitrary values of the mass parameters, where the quantization problem leads to resonant states. We also explore the relation between this correspondence and cluster integrable systems.

48 pages, 9 figures, minor typos corrected

References in corpus (44)

• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Geometric Engineering of Quantum Field Theories
• Topological Strings and Integrable Hierarchies
• The Refined Topological Vertex
• From weak to strong coupling in ABJM theory
• Discrete Heisenberg-Weyl Group and Modular Group
• Quantum Dilogarithm
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• ABJM theory as a Fermi gas
• Disk Instantons, Mirror Symmetry and the Duality Web
• Non-perturbative effects and the refined topological string
• Exact Results in ABJM Theory from Topological Strings
• Quantum Geometry of Refined Topological Strings
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Instanton Bound States in ABJM Theory
• Exact Results on the ABJM Fermi Gas
• Extended Holomorphic Anomaly in Gauge Theory
• Matrix models from operators and topological strings, 2
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Operators from mirror curves and the quantum dilogarithm
• Matrix models from operators and topological strings
• Exact ABJM Partition Function from TBA
• Topological Strings and Quantum Spectral Problems
• Exact quantization conditions for the relativistic Toda lattice
• Lectures on Mirror Symmetry
• Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• Dimer Models and Integrable Systems
• Exact quantization conditions for cluster integrable systems
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
• Quantization condition from exact WKB for difference equations
• TBA-like integral equations from quantized mirror curves
• Exact results for topological strings on resolved Y(p,q) singularities
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• Exact eigenfunctions and the open topological string
• Lie Groups, Cluster Variables and Integrable Systems
• Loop groups, Clusters, Dimers and Integrable systems
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Spectral determinants and quantum theta functions
• Algebraic K-theory of toric hypersurfaces
• Geometric transition in Non-perturbative Topological string

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• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Peacock patterns and new integer invariants in topological string theory
• A Solvable Deformation of Quantum Mechanics
• Exact WKB methods in $SU(2)$ $N_f=1$
• Exact eigenfunctions and the open topological string
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• Calabi-Yau geometry and electrons on 2d lattices
• BPS relations from spectral problems and blowup equations
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Hanany-Witten Transition in Quantum Curves
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Resonances and PT symmetry in quantum curves
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Brane Transitions from Exceptional Groups
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Matrix models for topological strings: exact results in the planar limit
• Quantum curves as quantum distributions
• Painlevé Kernels and Surface Defects at Strong Coupling
• Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves