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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
  • 18 Downloads

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 \( \mathcal{N} \) = 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 Theories Nonperturbative Effects Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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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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