Title

# TBA equations and resurgent Quantum Mechanics

Authors
Ito, Katsushi
Shu, Hongfei
Published in . 2019, vol. 1901, p. 228
Collection Open Access - SCOAP3
Abstract 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 N $$\mathcal{N}$$ = 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.
Keywords Integrable Field TheoriesNonperturbative EffectsTopological Field Theories
Identifiers
arXiv: 1811.04812
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(ISO format)
ITO, Katsushi, MARINO BEIRAS, Marcos, SHU, Hongfei. TBA equations and resurgent Quantum Mechanics. In: Journal of High Energy Physics, 2019, vol. 1901, p. 228. doi: 10.1007/JHEP01(2019)228 https://archive-ouverte.unige.ch/unige:114708

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