BPS relations from spectral problems and blowup equations

Abstract

Recently an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi-Yau threefolds has been proposed. At the same time an exact quantization condition for the cluster integrable systems associated to these geometries has been conjectured. The consistency between the two approaches leads to an infinite set of constraints for the refined BPS invariants of the toric Calabi-Yau threefolds. We prove these constraints for the $Y^{N,m}$ geometries using the $K$-theoretic blowup equations for $SU(N)$ SYM with generic Chern-Simons invariant $m$.

26 pages, 3 figures, 2 tables, a few typos corrected

References in corpus (12)

• The Refined Topological Vertex
• Open string amplitudes and large order behavior in topological string theory
• Remodeling the B-model
• Extended Holomorphic Anomaly in Gauge Theory
• Topological Strings and Quantum Spectral Problems
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Hofstadter's Butterfly in Quantum Geometry
• Operators and higher genus mirror curves
• ABJM on ellipsoid and topological strings
• Quantization condition from exact WKB for difference equations
• TBA-like integral equations from quantized mirror curves
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String

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• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Exponential Networks, WKB and Topological String
• Instantons from Blow-up
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Quantum spectral problems and isomonodromic deformations
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Irregular conformal blocks, Painlevé III and the blow-up equations
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• Resurgent Structure of the Topological String and the First Painlevé Equation
• Painlevé Kernels and Surface Defects at Strong Coupling