TBA equations and resurgent Quantum Mechanics
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 resu...
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doaj-8e756e0df90043a19cb664d70f237f632020-11-24T21:42:55ZengSpringerOpenJournal of High Energy Physics1029-84792019-01-012019114510.1007/JHEP01(2019)228TBA equations and resurgent Quantum MechanicsKatsushi Ito0Marcos Mariño1Hongfei Shu2Department of Physics, Tokyo Institute of TechnologyDépartement de Physique Théorique & Section de Mathématiques, Université de GenèveDepartment of Physics, Tokyo Institute of TechnologyAbstract 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.http://link.springer.com/article/10.1007/JHEP01(2019)228Integrable Field TheoriesNonperturbative EffectsTopological Field Theories |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Katsushi Ito Marcos Mariño Hongfei Shu |
spellingShingle |
Katsushi Ito Marcos Mariño Hongfei Shu TBA equations and resurgent Quantum Mechanics Journal of High Energy Physics Integrable Field Theories Nonperturbative Effects Topological Field Theories |
author_facet |
Katsushi Ito Marcos Mariño Hongfei Shu |
author_sort |
Katsushi Ito |
title |
TBA equations and resurgent Quantum Mechanics |
title_short |
TBA equations and resurgent Quantum Mechanics |
title_full |
TBA equations and resurgent Quantum Mechanics |
title_fullStr |
TBA equations and resurgent Quantum Mechanics |
title_full_unstemmed |
TBA equations and resurgent Quantum Mechanics |
title_sort |
tba equations and resurgent quantum mechanics |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-01-01 |
description |
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. |
topic |
Integrable Field Theories Nonperturbative Effects Topological Field Theories |
url |
http://link.springer.com/article/10.1007/JHEP01(2019)228 |
work_keys_str_mv |
AT katsushiito tbaequationsandresurgentquantummechanics AT marcosmarino tbaequationsandresurgentquantummechanics AT hongfeishu tbaequationsandresurgentquantummechanics |
_version_ |
1725916469501362176 |