Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries

Abstract

We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on genus one mirror curves. We compute the spectra of the quantum systems both by standard perturbation method and by Bohr-Sommerfeld method with quantum periods as the phase volumes. In this way, we obtain some exact analytic results for the classical and quantum periods of the Calabi-Yau geometries. We also determine the differential operators of the quantum periods and compute the topological string free energy in Nekrasov-Shatashvili (NS) limit. The results agree with calculations from other methods such as the topological vertex.

arXiv comment40 pages, 3 figures. v2: minor corrections, published in JHEP

References in corpus (44)

• Topological Strings and Integrable Hierarchies
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Brane Dimers and Quiver Gauge Theories
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Dimer models and toric diagrams
• Non-perturbative effects and the refined topological string
• Quantum Geometry of Refined Topological Strings
• Refined stable pair invariants for E-, M- and [p,q]-strings
• An introduction to the dimer model
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Topological Strings and Quantum Spectral Problems
• The Toric Phases of the Y^{p,q} Quivers
• Deformed N=2 theories, generalized recursion relations and S-duality
• Exact quantization conditions for the relativistic Toda lattice
• Counting Exceptional Instantons
• Dimer Models and Integrable Systems
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• Exact quantization conditions for cluster integrable systems
• Hofstadter's Butterfly in Quantum Geometry
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Operators and higher genus mirror curves
• Blowup Equations for 6d SCFTs. I
• Resurgence Matches Quantization
• A Solvable Deformation of Quantum Mechanics
• Quantization condition from exact WKB for difference equations
• Blowup Equations for Refined Topological Strings
• Deformed Seiberg-Witten Curves for ADE Quivers
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Double Bruhat Cells in Kac-Moody Groups and Integrable Systems
• Lie Groups, Cluster Variables and Integrable Systems
• Calabi-Yau geometry and electrons on 2d lattices
• Instantons from Blow-up
• BPS relations from spectral problems and blowup equations
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• WKB Method and Quantum Periods beyond Genus One
• Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves
• Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry

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• Dimers for Type D Relativistic Toda Model
• New dimer integrable systems and defects in five dimensional gauge theory
• Quantum Periods and TBA-like Equations for a Class of Calabi-Yau Geometries
• Birational Transformations on Dimer Integrable Systems