We study the WKB periods for the third order ordinary differential equation (ODE) with polynomial potential, which is obtained by the Nekrasov-Shatashvili limit of () Argyres-Douglas theory in the Omega background. In the minimal chamber of the moduli space, we derive the Y-system and the thermodynamic Bethe ansatz (TBA) equations by using the ODE/IM correspondence. The exact WKB periods are identified with the Y-functions. Varying the moduli parameters of the potential, the wall-crossing of the TBA equations occurs. We study the process of the wall-crossing from the minimal chamber to the maximal chamber for and . When the potential is a monomial type, we show the TBA equations obtained from the () and ()-type ODE lead to the and -type TBA equations respectively.
{ "license": [ { "url": "http://creativecommons.org/licenses/by/3.0/", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "statement": "The Author(s)", "year": "2022" } ], "control_number": "69221", "_oai": { "updated": "2023-10-13T18:31:19Z", "id": "oai:repo.scoap3.org:69221", "sets": [ "NPB" ] }, "authors": [ { "affiliations": [ { "country": "Japan", "value": "Department of Physics, Tokyo Institute of Technology, Tokyo, Japan" } ], "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, Japan" } ], "surname": "Kondo", "email": "t.kondo@th.phys.titech.ac.jp", "full_name": "Kondo, Takayasu", "given_names": "Takayasu" }, { "surname": "Shu", "given_names": "Hongfei", "affiliations": [ { "country": "China", "value": "Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, China" }, { "country": "China", "value": "Yau Mathematical Sciences Center (YMSC), Tsinghua University, Beijing, China" } ], "full_name": "Shu, Hongfei", "orcid": "0000-0003-1890-7762", "email": "shuphy124@gmail.com" } ], "_files": [ { "checksum": "md5:9d66208f46f9f3840b49b2738dab9a02", "filetype": "xml", "bucket": "e85f853f-82b5-4e99-bfa7-eb3696a56891", "version_id": "a08c5653-11a8-41c3-a940-bd60b1c646e2", "key": "10.1016/j.nuclphysb.2022.115788.xml", "size": 1439311 }, { "checksum": "md5:8b778e91b5910fb9458bbd75353e8330", "filetype": "pdf", "bucket": "e85f853f-82b5-4e99-bfa7-eb3696a56891", "version_id": "c4aff6d7-97a6-4e51-80f0-389f8a755399", "key": "10.1016/j.nuclphysb.2022.115788.pdf", "size": 1102276 }, { "checksum": "md5:847d95eb4b6550f91034d55bc752fa28", "filetype": "pdf/a", "bucket": "e85f853f-82b5-4e99-bfa7-eb3696a56891", "version_id": "092e7173-4b14-4970-9b84-12955ed55731", "key": "10.1016/j.nuclphysb.2022.115788_a.pdf", "size": 1206342 } ], "record_creation_date": "2022-04-15T12:30:42.844461", "titles": [ { "source": "Elsevier", "title": "Wall-crossing of TBA equations and WKB periods for the third order ODE" } ], "collections": [ { "primary": "Nuclear Physics B" } ], "dois": [ { "value": "10.1016/j.nuclphysb.2022.115788" } ], "publication_info": [ { "journal_volume": "971 C", "journal_title": "Nuclear Physics B", "material": "article", "artid": "115788", "year": 2022 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "abstracts": [ { "source": "Elsevier", "value": "We study the WKB periods for the third order ordinary differential equation (ODE) with polynomial potential, which is obtained by the Nekrasov-Shatashvili limit of (<math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi></mrow></msub></math>) Argyres-Douglas theory in the Omega background. In the minimal chamber of the moduli space, we derive the Y-system and the thermodynamic Bethe ansatz (TBA) equations by using the ODE/IM correspondence. The exact WKB periods are identified with the Y-functions. Varying the moduli parameters of the potential, the wall-crossing of the TBA equations occurs. We study the process of the wall-crossing from the minimal chamber to the maximal chamber for <math><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math> and <math><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math>. When the potential is a monomial type, we show the TBA equations obtained from the (<math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math>) and (<math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>3</mn></mrow></msub></math>)-type ODE lead to the <math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math> and <math><msub><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow></msub></math>-type TBA equations respectively." } ], "imprints": [ { "date": "2022-04-15", "publisher": "Elsevier" } ], "acquisition_source": { "date": "2023-10-13T18:30:39.150879", "source": "Elsevier", "method": "Elsevier", "submission_number": "8481822c69f611ee9688729695cabdc8" } }