We study the $$ {\mathfrak{gl}}_{m\mid n} $$ XXX spin chains defined on tensor products of highest weight $$ {\mathfrak{gl}}_{m\mid n} $$ -modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues. Then we take the classical limits and obtain the corresponding results for the $$ {\mathfrak{gl}}_{m\mid n} $$ Gaudin models.
{ "_oai": { "updated": "2023-07-25T00:31:05Z", "id": "oai:repo.scoap3.org:77229", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "USA", "value": "Department of Mathematics, University of Virginia, 141 Cabell Dr, Charlottesville, VA, 22903, USA", "organization": "University of Virginia" } ], "surname": "Lu", "email": "Kang.Lu@virginia.edu", "full_name": "Lu, Kang", "given_names": "Kang" } ], "titles": [ { "source": "Springer", "title": "On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains" } ], "dois": [ { "value": "10.1007/JHEP04(2023)120" } ], "publication_info": [ { "page_end": "40", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2023", "artid": "JHEP04(2023)120", "year": 2023, "page_start": "1", "journal_issue": "4" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-07-25T00:30:48.069522", "source": "Springer", "method": "Springer", "submission_number": "639de6b22a8211ee91ac6ee2827c7def" }, "page_nr": [ 40 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2023" } ], "control_number": "77229", "record_creation_date": "2023-04-26T03:30:09.971686", "_files": [ { "checksum": "md5:fc39bdf05265b342ddb8ffd09755851f", "filetype": "xml", "bucket": "21af2fba-30d8-40b4-9bcf-425d28305341", "version_id": "bb13b848-cb0d-40d5-82c9-c6824ba5294c", "key": "10.1007/JHEP04(2023)120.xml", "size": 11768 }, { "checksum": "md5:c7871ec37c7436a3cd50da129dadffd5", "filetype": "pdf/a", "bucket": "21af2fba-30d8-40b4-9bcf-425d28305341", "version_id": "3e5816ec-1807-47a6-85f8-b659c0ef9144", "key": "10.1007/JHEP04(2023)120_a.pdf", "size": 651107 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "math-ph", "math.MP" ], "value": "2209.14416" } ], "abstracts": [ { "source": "Springer", "value": "We study the <math> <msub> <mi>gl</mi> <mrow> <mi>m</mi> <mo>\u2223</mo> <mi>n</mi> </mrow> </msub> </math> $$ {\\mathfrak{gl}}_{m\\mid n} $$ XXX spin chains defined on tensor products of highest weight <math> <msub> <mi>gl</mi> <mrow> <mi>m</mi> <mo>\u2223</mo> <mi>n</mi> </mrow> </msub> </math> $$ {\\mathfrak{gl}}_{m\\mid n} $$ -modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues. Then we take the classical limits and obtain the corresponding results for the <math> <msub> <mi>gl</mi> <mrow> <mi>m</mi> <mo>\u2223</mo> <mi>n</mi> </mrow> </msub> </math> $$ {\\mathfrak{gl}}_{m\\mid n} $$ Gaudin models." } ], "imprints": [ { "date": "2023-04-24", "publisher": "Springer" } ] }