Poisson-Lie T-duality of WZW model via current algebra deformation

Francesco Bascone (INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy; Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy) ; Franco Pezzella (INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy) ; Patrizia Vitale (INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy; Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, Napoli, 80126, Italy)

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 su 2 a $$ \mathfrak{su}(2)\left(\mathrm{\mathbb{R}}\right)\overset{\cdot }{\oplus}\mathfrak{a} $$ , to the fully semisimple Kac-Moody algebra sl 2 $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{C}}\right)\left(\mathrm{\mathbb{R}}\right) $$ . 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.

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      "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."
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Published on:
08 September 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 9
Pages 1-46
DOI:
https://doi.org/10.1007/JHEP09(2020)060
arXiv:
2004.12858
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: