TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics
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,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-03-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2024)122 |
| _version_ | 1827205528027136000 |
|---|---|
| author | Katsushi Ito Hongfei Shu |
| author_facet | Katsushi Ito Hongfei Shu |
| author_sort | Katsushi Ito |
| collection | DOAJ |
| description | 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 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. |
| first_indexed | 2024-04-24T19:59:58Z |
| format | Article |
| id | doaj.art-19c834a838674e58acbe4b200d331967 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-21T12:09:42Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-19c834a838674e58acbe4b200d3319672024-06-30T11:08:55ZengSpringerOpenJournal of High Energy Physics1029-84792024-03-012024312710.1007/JHEP03(2024)122TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanicsKatsushi Ito0Hongfei Shu1Department of Physics, Tokyo Institute of TechnologySchool of Physics and Microelectronics, Zhengzhou UniversityAbstract 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 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.https://doi.org/10.1007/JHEP03(2024)122Bethe AnsatzIntegrable Field TheoriesNonperturbative EffectsSupersymmetric Effective Theories |
| spellingShingle | Katsushi Ito Hongfei Shu TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics Journal of High Energy Physics Bethe Ansatz Integrable Field Theories Nonperturbative Effects Supersymmetric Effective Theories |
| title | TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics |
| title_full | TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics |
| title_fullStr | TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics |
| title_full_unstemmed | TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics |
| title_short | TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics |
| title_sort | tba equations and exact wkb analysis in deformed supersymmetric quantum mechanics |
| topic | Bethe Ansatz Integrable Field Theories Nonperturbative Effects Supersymmetric Effective Theories |
| url | https://doi.org/10.1007/JHEP03(2024)122 |
| work_keys_str_mv | AT katsushiito tbaequationsandexactwkbanalysisindeformedsupersymmetricquantummechanics AT hongfeishu tbaequationsandexactwkbanalysisindeformedsupersymmetricquantummechanics |