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Annales Henri Poincaré

, Volume 20, Issue 2, pp 543–603 | Cite as

Non-perturbative Quantum Mechanics from Non-perturbative Strings

  • Santiago Codesido
  • Marcos MariñoEmail author
  • Ricardo Schiappa
Article
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Abstract

This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of topological string theory. The method can be applied to traditional spectral problems governed by the Schrödinger equation, where it both reproduces and extends the results of well-established approaches, such as the exact WKB method. It can be also applied to spectral problems based on the quantization of mirror curves, where it leads to new results on the trans-series structure of the spectrum. Various examples are discussed, including the modified Mathieu equation, the double-well potential and the quantum mirror curves of local \({\mathbb {P}}^2\) and local \({\mathbb {F}}_0\). In all these examples, it is verified in detail that the trans-series obtained with this new method correctly predict the large-order behavior of the corresponding perturbative sectors.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Santiago Codesido
    • 1
  • Marcos Mariño
    • 1
    Email author
  • Ricardo Schiappa
    • 2
    • 3
  1. 1.Département de Physique Théorique and Section de MathématiquesUniversité de GenèveGeneveSwitzerland
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraUSA
  3. 3.CAMGSD, Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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