Non-Abelian target space duals of Thurston geometries
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911052300550144 |
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| author | Eghbali, Ali Feizi, Mahsa Rezaei-Aghdam, Adel |
| author_facet | Eghbali, Ali Feizi, Mahsa Rezaei-Aghdam, Adel |
| contents | In this study, we proceed to investigate the Thurston geometries from the point of view of their Poisson-Lie (PL) T-dualizability. First of all, we find all subalgebras of Killing vectors that generate group of isometries acting freely and transitively on the three-dimensional target manifolds, where the Thurston metrics are defined. It is shown that three-dimensional Lie subalgebras are isomorphic to the Bianchi type algebras. We take the isometry subgroup of the metric as the first subgroup of Drinfeld double. In order to investigate the non-Abelian T-duality, the second subgroup must be chosen to be Abelian. Accordingly, the non-Abelian target space duals of these geometries are found via PL T-duality approach in the absence of $B$-field. We also comment on the conformal invariance conditions of the T-dual $σ$-models under consideration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Abelian target space duals of Thurston geometries Eghbali, Ali Feizi, Mahsa Rezaei-Aghdam, Adel High Energy Physics - Theory In this study, we proceed to investigate the Thurston geometries from the point of view of their Poisson-Lie (PL) T-dualizability. First of all, we find all subalgebras of Killing vectors that generate group of isometries acting freely and transitively on the three-dimensional target manifolds, where the Thurston metrics are defined. It is shown that three-dimensional Lie subalgebras are isomorphic to the Bianchi type algebras. We take the isometry subgroup of the metric as the first subgroup of Drinfeld double. In order to investigate the non-Abelian T-duality, the second subgroup must be chosen to be Abelian. Accordingly, the non-Abelian target space duals of these geometries are found via PL T-duality approach in the absence of $B$-field. We also comment on the conformal invariance conditions of the T-dual $σ$-models under consideration. |
| title | Non-Abelian target space duals of Thurston geometries |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.01797 |