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Thermodynamic Bethe ansatz and wall crossing for deformed supersymmetric quantum mechanics

Hongfei Shu1,*, Katsushi Ito2,†, and Jingjing Yang2,3,4,‡

  • *Contact author: shu@zzu.edu.cn
  • †Contact author: ito@th.phys.titech.ac.jp
  • ‡Contact author: jj150632@mail.ustc.edu.cn
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Phys. Rev. D 113, 046002 – Published 2 February, 2026

DOI: https://doi.org/10.1103/7r3h-lmwg

Abstract

We study the deformed supersymmetric quantum mechanics with a polynomial superpotential with ℏ correction. In the minimal chamber, where all turning points are real and distinct, it was shown that the exact Wentzel–Kramers–Brillouin periods obey the Z4-extended thermodynamic Bethe ansatz (TBA) equations of the undeformed potential. By changing the energy parameter above/below the critical points, the turning points become complex, and the moduli are outside of the minimal chamber. We study the wall crossing of the Z4-extended TBA equations by this change of moduli and show that the Z4 structure is preserved after the wall crossing. In particular, the TBA equations for the cubic superpotential are studied in detail, where there are two chambers (minimal and maximal). At the maximally symmetric point in the maximal chamber, the TBA system becomes the two sets of the D3-type TBA equations, which are regarded as the Z4 extension of the A3/Z2-type TBA equation.

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Phys. Rev. D 113, 046002– Published 2 February, 2026
  • Received 23 October 2025
  • Accepted 5 January 2026
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