High Energy Physics - Theory
[Submitted on 12 Nov 2018 (v1), last revised 31 Jan 2019 (this version, v3)]
Title:TBA equations and resurgent Quantum Mechanics
View PDFAbstract:We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded as the solution of a Riemann-Hilbert problem in resurgent Quantum Mechanics formulated by Voros. Our derivation builds upon the solution of similar Riemann-Hilbert problems in the study of BPS spectra in $\mathcal{N}=2$ gauge theories and of minimal surfaces in AdS. We also show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. We illustrate our general analysis with a detailed study of PT-symmetric cubic oscillators and quartic oscillators.
Submission history
From: Hongfei Shu [view email][v1] Mon, 12 Nov 2018 15:46:56 UTC (3,291 KB)
[v2] Tue, 20 Nov 2018 11:48:07 UTC (3,291 KB)
[v3] Thu, 31 Jan 2019 10:41:58 UTC (3,707 KB)
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