WKB periods for higher order ODE and TBA equations

Katsushi Ito (Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan) ; Takayasu Kondo (Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan) ; Kohei Kuroda (Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan) ; Hongfei Shu (Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, 101408, China; Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, Stockholm, SE-106 91, Sweden)

We study the WKB periods for the (r + 1)-th order ordinary differential equation (ODE) which is obtained by the conformal limit of the linear problem associated with the A r 1 $$ {A}_r^{(1)} $$ affine Toda field equation. We compute the quantum corrections by using the Picard-Fuchs operators. The ODE/IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation related to the Lie algebra A r . For the quadratic potential, we propose a formula to show the equivalence between the logarithm of the Y-function and the WKB period, which is confirmed by solving the TBA equation numerically.

{
  "_oai": {
    "updated": "2022-01-24T12:52:10Z", 
    "id": "oai:repo.scoap3.org:65508", 
    "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": "Japan", 
          "value": "Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan", 
          "organization": "Tokyo Institute of Technology"
        }
      ], 
      "surname": "Kondo", 
      "email": "t.kondo@th.phys.titech.ac.jp", 
      "full_name": "Kondo, Takayasu", 
      "given_names": "Takayasu"
    }, 
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan", 
          "organization": "Tokyo Institute of Technology"
        }
      ], 
      "surname": "Kuroda", 
      "email": "k.kuroda@th.phys.titech.ac.jp", 
      "full_name": "Kuroda, Kohei", 
      "given_names": "Kohei"
    }, 
    {
      "affiliations": [
        {
          "country": "China", 
          "value": "Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, 101408, China", 
          "organization": "Beijing Institute of Mathematical Sciences and Applications (BIMSA)"
        }, 
        {
          "country": "Sweden", 
          "value": "Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, Stockholm, SE-106 91, Sweden", 
          "organization": "Nordita, KTH Royal Institute of Technology and Stockholm University"
        }
      ], 
      "surname": "Shu", 
      "email": "hongfei.shu@su.se", 
      "full_name": "Shu, Hongfei", 
      "given_names": "Hongfei"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "WKB periods for higher order ODE and TBA equations"
    }
  ], 
  "dois": [
    {
      "value": "10.1007/JHEP10(2021)167"
    }
  ], 
  "publication_info": [
    {
      "page_end": "29", 
      "journal_title": "Journal of High Energy Physics", 
      "material": "article", 
      "journal_volume": "2021", 
      "artid": "JHEP10(2021)167", 
      "year": 2021, 
      "page_start": "1", 
      "journal_issue": "10"
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
  "acquisition_source": {
    "date": "2022-01-24T00:34:54.861853", 
    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "c3b70ed27cac11ec9421ee5ceb395428"
  }, 
  "page_nr": [
    29
  ], 
  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2021"
    }
  ], 
  "control_number": "65508", 
  "record_creation_date": "2021-10-22T12:30:20.092606", 
  "_files": [
    {
      "checksum": "md5:1b0d4634087dec26e550297601194e30", 
      "filetype": "xml", 
      "bucket": "fa07d03b-cc4c-4979-92f0-24286a5eee09", 
      "version_id": "2464333c-4a36-410b-b915-18ee892dfce6", 
      "key": "10.1007/JHEP10(2021)167.xml", 
      "size": 13890
    }, 
    {
      "checksum": "md5:eb9a9047c226ef6efa79b2ab9c18f02c", 
      "filetype": "pdf/a", 
      "bucket": "fa07d03b-cc4c-4979-92f0-24286a5eee09", 
      "version_id": "ce4897a4-6fdb-4cf5-8466-92f66eba187d", 
      "key": "10.1007/JHEP10(2021)167_a.pdf", 
      "size": 513654
    }
  ], 
  "collections": [
    {
      "primary": "Journal of High Energy Physics"
    }
  ], 
  "arxiv_eprints": [
    {
      "value": "2104.13680"
    }
  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "We study the WKB periods for the (r + 1)-th order ordinary differential equation (ODE) which is obtained by the conformal limit of the linear problem associated with the   <math> <msubsup> <mi>A</mi> <mi>r</mi> <mfenced> <mn>1</mn> </mfenced> </msubsup> </math>  $$ {A}_r^{(1)} $$  affine Toda field equation. We compute the quantum corrections by using the Picard-Fuchs operators. The ODE/IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation related to the Lie algebra A  r . For the quadratic potential, we propose a formula to show the equivalence between the logarithm of the Y-function and the WKB period, which is confirmed by solving the TBA equation numerically."
    }
  ], 
  "imprints": [
    {
      "date": "2021-10-20", 
      "publisher": "Springer"
    }
  ]
}
Published on:
20 October 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 10
Pages 1-29
DOI:
https://doi.org/10.1007/JHEP10(2021)167
arXiv:
2104.13680
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: