Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality
Abstract By calculating inequivalent classical r-matrices for the $$gl(2,{\mathbb {R}})$$ g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) Lie...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-12084-8 |
| _version_ | 1797247081099821056 |
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| author | Ali Eghbali Tayebe Parvizi Adel Rezaei-Aghdam |
| author_facet | Ali Eghbali Tayebe Parvizi Adel Rezaei-Aghdam |
| author_sort | Ali Eghbali |
| collection | DOAJ |
| description | Abstract By calculating inequivalent classical r-matrices for the $$gl(2,{\mathbb {R}})$$ g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) Lie group in twelve inequivalent families. Most importantly, it is shown that each of these models can be obtained from a Poisson-Lie T-dual $$\sigma $$ σ -model in the presence of the spectator fields when the dual Lie group is considered to be Abelian, i.e. all deformed models have Poisson-Lie symmetry just as undeformed WZW model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) . In this way, all deformed models are specified via spectator-dependent background matrices. For one case, the dual background is clearly found. |
| first_indexed | 2024-03-11T18:21:19Z |
| format | Article |
| id | doaj.art-9ce327377ec04376b78194192f5627b4 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T19:53:01Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-9ce327377ec04376b78194192f5627b42024-03-24T12:30:26ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-10-01831011210.1140/epjc/s10052-023-12084-8Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-dualityAli Eghbali0Tayebe Parvizi1Adel Rezaei-Aghdam2Department of Physics, Faculty of Basic Sciences, Azarbaijan Shahid Madani UniversityDepartment of Physics, Faculty of Basic Sciences, Azarbaijan Shahid Madani UniversityDepartment of Physics, Faculty of Basic Sciences, Azarbaijan Shahid Madani UniversityAbstract By calculating inequivalent classical r-matrices for the $$gl(2,{\mathbb {R}})$$ g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) Lie group in twelve inequivalent families. Most importantly, it is shown that each of these models can be obtained from a Poisson-Lie T-dual $$\sigma $$ σ -model in the presence of the spectator fields when the dual Lie group is considered to be Abelian, i.e. all deformed models have Poisson-Lie symmetry just as undeformed WZW model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) . In this way, all deformed models are specified via spectator-dependent background matrices. For one case, the dual background is clearly found.https://doi.org/10.1140/epjc/s10052-023-12084-8 |
| spellingShingle | Ali Eghbali Tayebe Parvizi Adel Rezaei-Aghdam Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality European Physical Journal C: Particles and Fields |
| title | Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality |
| title_full | Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality |
| title_fullStr | Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality |
| title_full_unstemmed | Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality |
| title_short | Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality |
| title_sort | yang baxter deformations of the gl 2 mathbb r g l 2 r wzw model and non abelian t duality |
| url | https://doi.org/10.1140/epjc/s10052-023-12084-8 |
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