Operators and higher genus mirror curves

TL;DR

This paper investigates the spectral theory and topological string correspondence for higher genus mirror curves with nontrivial mass parameters, providing evidence for its validity across various geometries and exploring connections to integrable systems.

Contribution

It extends the spectral-topological string correspondence to higher genus mirror curves with mass parameters and explores its relation to cluster integrable systems.

Findings

The correspondence holds for geometries like SU(3) relativistic Toda and C^3/Z_6 orbifold.

Evidence suggests the correspondence is valid for arbitrary mass parameters.

The study links the spectral-topological string relation to cluster integrable systems.

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.