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 $$ {A}_r^{(1)} $$ 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" } ] }