# Resonances and PT symmetry in quantum curves

## TL;DR

This paper explores the spectral properties of non-Hermitian quantum curves with complex spectra, focusing on PT symmetry and resonance phenomena, and develops computational techniques to test theoretical predictions in this area.

## Contribution

It introduces methods to compute complex spectra of quantum curves and analyzes PT-symmetric quantum Seiberg-Witten curves with spontaneous PT-symmetry breaking.

## Key findings

- Developed techniques for spectral computation of non-Hermitian quantum curves
- Provided tests for predictions of spectral properties in PT-symmetric systems
- Analyzed exactly solvable PT-symmetric Seiberg-Witten curves

## Abstract

In the correspondence between spectral problems and topological strings, it is natural to consider complex values for the string theory moduli. In the spectral theory side, this corresponds to non-Hermitian quantum curves with complex spectra and resonances, and in some cases, to PT-symmetric spectral problems. The correspondence leads to precise predictions about the spectral properties of these non-Hermitian operators. In this paper we develop techniques to compute the complex spectra of these quantum curves, providing in this way precision tests of these predictions. In addition, we analyze quantum Seiberg-Witten curves with PT symmetry, which provide interesting and exactly solvable examples of spontaneous PT-symmetry breaking.