Abstract
We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian.
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Acknowledgments
We would like to thank Daniele Gregori, Syo Kamata, Yong Li, Marco Rossi, JingJing Yang and Hao Zou for useful discussions. The work of K.I. is supported in part by Grant-in-Aid for Scientific Research 21K03570 from Japan Society for the Promotion of Science (JSPS). The work of H.S. is supported by the Start-up Funding of Zhengzhou University. H.S. would like to thank Tokyo Institute of Technology for their hospitality.
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Ito, K., Shu, H. TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics. J. High Energ. Phys. 2024, 122 (2024). https://doi.org/10.1007/JHEP03(2024)122
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DOI: https://doi.org/10.1007/JHEP03(2024)122