Resonances and PT symmetry in quantum 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.

arXiv commentclarifications and references added

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Cited by in corpus (7)

• Exact WKB methods in $SU(2)$ $N_f=1$
• TBA Equations and Quantization Conditions
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Exact WKB analysis for $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics: Study of the Ai-Bender-Sarkar conjecture
• Quantization of Harer-Zagier formulas
• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons