Resonances and PT symmetry in quantum curves

Understand

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.