Journal of High Energy Physics

, 2019:228 | Cite as

TBA equations and resurgent Quantum Mechanics

  • Katsushi Ito
  • Marcos Mariño
  • Hongfei ShuEmail author
Open Access
Regular Article - Theoretical Physics


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.


Integrable Field Theories Nonperturbative Effects Topological Field Theories 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsTokyo Institute of TechnologyTokyoJapan
  2. 2.Département de Physique Théorique & Section de MathématiquesUniversité de GenèveGenèveSwitzerland

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