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TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics

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arxiv 2401.03766 v2 pith:FNJ5EMS5 submitted 2024-01-08 hep-th math-phmath.MP

Katsushi Ito , Hongfei Shu This is my paper
classification hep-thmath-phmath.MP
keywords equationsdeformedexactfindmechanicspotentialquantumsuperpotential
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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 Schr\"odinger 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 ${\mathbb Z}_4$-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two $D_3$-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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Cited by 3 Pith papers

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  1. Exact WKB in all sectors II: Potentials with non-degenerate saddles

    hep-th 2025-11 conditional novelty 7.0 of 10

    For generic one-dimensional potentials, the exact spectrum decomposes into as many trans-series sectors as there are distinct local-minimum energy levels, with continuous transitions across barrier tops and discontinu...

  2. Exact WKB of solutions by Borel summation and open TBA

    hep-th 2025-07 conditional novelty 7.0 of 10

    Borel-summed WKB solutions of quantum Seiberg-Witten equations are matched, numerically, to GMN open TBA solutions for the Weber and modified Mathieu equations.

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    physics.ins-det 2025-08 unverdicted novelty 4.0 of 10

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