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 (7)

• The Refined Topological Vertex
• Extended Holomorphic Anomaly in Gauge Theory
• Exact ABJM Partition Function from TBA
• Topological Strings and Quantum Spectral Problems
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Algebraic K-theory of toric hypersurfaces
• Geometric transition in Non-perturbative Topological string

Cited by in corpus (5)

• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• 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