Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of SU(2) as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $$ \mathfrak{su}(2)\left(\mathrm{\mathbb{R}}\right)\overset{\cdot }{\oplus}\mathfrak{a} $$ , to the fully semisimple Kac-Moody algebra $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{C}}\right)\left(\mathrm{\mathbb{R}}\right) $$ . A two-parameter family of models with SL(2, ℂ) as target phase space is obtained so that Poisson-Lie T-duality is realised as an O(3, 3) rotation in the phase space. The dual family shares the same phase space but its configuration space is SB(2, ℂ), the Poisson-Lie dual of the group SU(2). A parent action with doubled degrees of freedom on SL(2, ℂ) is defined, together with its Hamiltonian description.
{ "_oai": { "updated": "2021-01-25T17:53:01Z", "id": "oai:repo.scoap3.org:56850", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Italy", "value": "INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy", "organization": "INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6" }, { "country": "Italy", "value": "Dipartimento di Fisica \u201cE. Pancini\u201d, Universit\u00e0 di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy", "organization": "Dipartimento di Fisica \u201cE. Pancini\u201d, Universit\u00e0 di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6" } ], "surname": "Bascone", "email": "francesco.bascone@na.infn.it", "full_name": "Bascone, Francesco", "given_names": "Francesco" }, { "affiliations": [ { "country": "Italy", "value": "INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy", "organization": "INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6" } ], "surname": "Pezzella", "email": "franco.pezzella@na.infn.it", "full_name": "Pezzella, Franco", "given_names": "Franco" }, { "affiliations": [ { "country": "Italy", "value": "INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy", "organization": "INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6" }, { "country": "Italy", "value": "Dipartimento di Fisica \u201cE. Pancini\u201d, Universit\u00e0 di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy", "organization": "Dipartimento di Fisica \u201cE. Pancini\u201d, Universit\u00e0 di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6" } ], "surname": "Vitale", "email": "patrizia.vitale@na.infn.it", "full_name": "Vitale, Patrizia", "given_names": "Patrizia" } ], "titles": [ { "source": "Springer", "title": "Poisson-Lie T-duality of WZW model via current algebra deformation" } ], "dois": [ { "value": "10.1007/JHEP09(2020)060" } ], "publication_info": [ { "page_end": "46", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2020", "artid": "JHEP09(2020)060", "year": 2020, "page_start": "1", "journal_issue": "9" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2020-12-25T01:31:02.654592", "source": "Springer", "method": "Springer", "submission_number": "5299df22464811ebbd0e02163e01809a" }, "page_nr": [ 46 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2020" } ], "control_number": "56850", "record_creation_date": "2020-09-09T14:30:26.012386", "_files": [ { "checksum": "md5:2bab455e1ed7f380b7a73d662ffb2f2a", "filetype": "xml", "bucket": "38b7d73f-9728-4489-a89e-416ddccf6622", "version_id": "70fcd965-8885-4762-9e38-d441486cbf4a", "key": "10.1007/JHEP09(2020)060.xml", "size": 13538 }, { "checksum": "md5:73b39729d2ee3ac1553d9e3f5c3c8f2a", "filetype": "pdf/a", "bucket": "38b7d73f-9728-4489-a89e-416ddccf6622", "version_id": "eec18fe0-f963-4a83-838d-9010e0b899e3", "key": "10.1007/JHEP09(2020)060_a.pdf", "size": 693385 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "math-ph", "math.MP" ], "value": "2004.12858" } ], "abstracts": [ { "source": "Springer", "value": "Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of SU(2) as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum <math> <mi>su</mi> <mfenced> <mn>2</mn> </mfenced> <mfenced> <mi>\u211d</mi> </mfenced> <mover> <mo>\u2295</mo> <mo>\u22c5</mo> </mover> <mi>a</mi> </math> $$ \\mathfrak{su}(2)\\left(\\mathrm{\\mathbb{R}}\\right)\\overset{\\cdot }{\\oplus}\\mathfrak{a} $$ , to the fully semisimple Kac-Moody algebra <math> <mi>sl</mi> <mfenced> <mn>2</mn> <mi>\u2102</mi> </mfenced> <mfenced> <mi>\u211d</mi> </mfenced> </math> $$ \\mathfrak{sl}\\left(2,\\mathrm{\\mathbb{C}}\\right)\\left(\\mathrm{\\mathbb{R}}\\right) $$ . A two-parameter family of models with SL(2, \u2102) as target phase space is obtained so that Poisson-Lie T-duality is realised as an O(3, 3) rotation in the phase space. The dual family shares the same phase space but its configuration space is SB(2, \u2102), the Poisson-Lie dual of the group SU(2). A parent action with doubled degrees of freedom on SL(2, \u2102) is defined, together with its Hamiltonian description." } ], "imprints": [ { "date": "2020-09-08", "publisher": "Springer" } ] }