TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics

Katsushi Ito (Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan) ; Hongfei Shu (School of Physics and Microelectronics, Zhengzhou University, Zhengzhou, Henan, 450001, China; Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408, China; Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China)

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.

{
  "_oai": {
    "updated": "2024-06-24T00:32:22Z", 
    "id": "oai:repo.scoap3.org:84185", 
    "sets": [
      "JHEP"
    ]
  }, 
  "authors": [
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan", 
          "organization": "Tokyo Institute of Technology"
        }
      ], 
      "surname": "Ito", 
      "email": "ito@th.phys.titech.ac.jp", 
      "full_name": "Ito, Katsushi", 
      "given_names": "Katsushi"
    }, 
    {
      "affiliations": [
        {
          "country": "China", 
          "value": "School of Physics and Microelectronics, Zhengzhou University, Zhengzhou, Henan, 450001, China", 
          "organization": "Zhengzhou University"
        }, 
        {
          "country": "China", 
          "value": "Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408, China", 
          "organization": "Beijing Institute of Mathematical Sciences and Applications"
        }, 
        {
          "country": "China", 
          "value": "Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China", 
          "organization": "Tsinghua University"
        }
      ], 
      "surname": "Shu", 
      "email": "shu@zzu.edu.cn", 
      "full_name": "Shu, Hongfei", 
      "given_names": "Hongfei"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics"
    }
  ], 
  "dois": [
    {
      "value": "10.1007/JHEP03(2024)122"
    }
  ], 
  "publication_info": [
    {
      "page_end": "27", 
      "journal_title": "Journal of High Energy Physics", 
      "material": "article", 
      "journal_volume": "2024", 
      "artid": "JHEP03(2024)122", 
      "year": 2024, 
      "page_start": "1", 
      "journal_issue": "3"
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
  "acquisition_source": {
    "date": "2024-06-24T00:31:19.849190", 
    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "e40b131a31c011ef9fecbe60ec5a7b90"
  }, 
  "page_nr": [
    27
  ], 
  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2024"
    }
  ], 
  "control_number": "84185", 
  "record_creation_date": "2024-03-21T03:30:10.288539", 
  "_files": [
    {
      "checksum": "md5:25a5cdc9b5fe4ea14301f3f0d2ef7f52", 
      "filetype": "xml", 
      "bucket": "4f235c88-f5a5-4340-97f4-75520e958e9f", 
      "version_id": "2b1b2e9e-82bd-451f-b9d8-2c40f81befcd", 
      "key": "10.1007/JHEP03(2024)122.xml", 
      "size": 12137
    }, 
    {
      "checksum": "md5:c8d9182a030ca5611d1689557ca9e949", 
      "filetype": "pdf/a", 
      "bucket": "4f235c88-f5a5-4340-97f4-75520e958e9f", 
      "version_id": "dd002e98-615f-4b8e-ba5d-a398c8f1ae89", 
      "key": "10.1007/JHEP03(2024)122_a.pdf", 
      "size": 612507
    }
  ], 
  "collections": [
    {
      "primary": "Journal of High Energy Physics"
    }
  ], 
  "arxiv_eprints": [
    {
      "categories": [
        "hep-th", 
        "math-ph", 
        "math.MP"
      ], 
      "value": "2401.03766"
    }
  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "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\u00f6dinger 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 \u21244-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."
    }
  ], 
  "imprints": [
    {
      "date": "2024-03-20", 
      "publisher": "Springer"
    }
  ]
}
Published on:
20 March 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 3
Pages 1-27
DOI:
https://doi.org/10.1007/JHEP03(2024)122
arXiv:
2401.03766
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: