Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality
Abstract We proceed to investigate the non-Abelian T-duality of $$AdS_{2}$$ A d S 2 , $$AdS_{2}\times S^1$$ A d S 2 × S 1 and $$AdS_{3}$$ A d S 3 physical backgrounds, as well as the metric of the analytic continuation of $$AdS_{2}$$ A d S 2 from the point of view of Poisson-Lie (PL) T-duality. To t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-10537-0 |
| _version_ | 1818158469149097984 |
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| author | Ali Eghbali Reza Naderi Adel Rezaei-Aghdam |
| author_facet | Ali Eghbali Reza Naderi Adel Rezaei-Aghdam |
| author_sort | Ali Eghbali |
| collection | DOAJ |
| description | Abstract We proceed to investigate the non-Abelian T-duality of $$AdS_{2}$$ A d S 2 , $$AdS_{2}\times S^1$$ A d S 2 × S 1 and $$AdS_{3}$$ A d S 3 physical backgrounds, as well as the metric of the analytic continuation of $$AdS_{2}$$ A d S 2 from the point of view of Poisson-Lie (PL) T-duality. To this end, we reconstruct these metrics of the AdS families as backgrounds of non-linear $$\sigma $$ σ -models on two- and three-dimensional Lie groups. By considering the Killing vectors of these metrics and by taking into account the fact that the subgroups of isometry Lie group of the metrics can be taken as one of the subgroups of the Drinfeld double (with Abelian duals) we look up the PL T-duality. To construct the dualizable metrics by the PL T-duality we find all subalgebras of Killing vectors that generate subgroup of isometries which acts freely and transitively on the manifolds defined by aforementioned AdS families. We then obtain the dual backgrounds for these families of AdS in such a way that we apply the usual rules of PL T-duality without further corrections. We have also investigated the conformal invariance conditions of the original backgrounds (AdS families) and their dual counterparts. Finally, by using the T-duality rules proposed by Kaloper and Meissner (KM) we calculate the Abelian T-duals of BTZ black hole up to two-loop by dualizing on the coordinates $$ \varphi $$ φ and t. When the dualizing is implemented by the shift of direction $$\varphi $$ φ , we show that the horizons and singularity of the dual spacetime are the same as in charged black string derived by Horne and Horowitz without $$\alpha '$$ α ′ -corrections, whereas in dualizing on the coordinate t we find a new three-dimensional black string whose structure and asymptotic nature are clearly determined. For this case, we show that the T-duality transformation changes the asymptotic behavior from $$AdS_3$$ A d S 3 to flat. |
| first_indexed | 2024-12-11T15:30:35Z |
| format | Article |
| id | doaj.art-cf20478ca32e4881ac371d71bb33f5fb |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-12-11T15:30:35Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-cf20478ca32e4881ac371d71bb33f5fb2022-12-22T01:00:05ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522022-07-0182711710.1140/epjc/s10052-022-10537-0Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-dualityAli Eghbali0Reza Naderi1Adel 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 We proceed to investigate the non-Abelian T-duality of $$AdS_{2}$$ A d S 2 , $$AdS_{2}\times S^1$$ A d S 2 × S 1 and $$AdS_{3}$$ A d S 3 physical backgrounds, as well as the metric of the analytic continuation of $$AdS_{2}$$ A d S 2 from the point of view of Poisson-Lie (PL) T-duality. To this end, we reconstruct these metrics of the AdS families as backgrounds of non-linear $$\sigma $$ σ -models on two- and three-dimensional Lie groups. By considering the Killing vectors of these metrics and by taking into account the fact that the subgroups of isometry Lie group of the metrics can be taken as one of the subgroups of the Drinfeld double (with Abelian duals) we look up the PL T-duality. To construct the dualizable metrics by the PL T-duality we find all subalgebras of Killing vectors that generate subgroup of isometries which acts freely and transitively on the manifolds defined by aforementioned AdS families. We then obtain the dual backgrounds for these families of AdS in such a way that we apply the usual rules of PL T-duality without further corrections. We have also investigated the conformal invariance conditions of the original backgrounds (AdS families) and their dual counterparts. Finally, by using the T-duality rules proposed by Kaloper and Meissner (KM) we calculate the Abelian T-duals of BTZ black hole up to two-loop by dualizing on the coordinates $$ \varphi $$ φ and t. When the dualizing is implemented by the shift of direction $$\varphi $$ φ , we show that the horizons and singularity of the dual spacetime are the same as in charged black string derived by Horne and Horowitz without $$\alpha '$$ α ′ -corrections, whereas in dualizing on the coordinate t we find a new three-dimensional black string whose structure and asymptotic nature are clearly determined. For this case, we show that the T-duality transformation changes the asymptotic behavior from $$AdS_3$$ A d S 3 to flat.https://doi.org/10.1140/epjc/s10052-022-10537-0 |
| spellingShingle | Ali Eghbali Reza Naderi Adel Rezaei-Aghdam Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality European Physical Journal C: Particles and Fields |
| title | Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality |
| title_full | Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality |
| title_fullStr | Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality |
| title_full_unstemmed | Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality |
| title_short | Non-Abelian T-duality of $$AdS_{d\le 3}$$ A d S d ≤ 3 families by Poisson-Lie T-duality |
| title_sort | non abelian t duality of ads d le 3 a d s d ≤ 3 families by poisson lie t duality |
| url | https://doi.org/10.1140/epjc/s10052-022-10537-0 |
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