$AdS_3 \times S^3$ Background from Poisson-Lie T-Duality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910657834647552 |
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| author | Eghbali, Ali |
| author_facet | Eghbali, Ali |
| contents | We proceed to construct a dual pair for the $AdS_3 \times S^3$ background by applying non-Abelian T-duality (here as Poisson-Lie (PL) T-duality on a semi-Abelian double). By using a certain parametrization of the $4$-dimensional Lie group ${A}_2 \otimes 2{A}_1$ and by a suitable choice of spectator-dependent matrices, the original $σ$-model including the $AdS_3 \times S^3$ metric and a non-trivial $B$-field are constructed. The dual background constructed by means of the PL T-duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non-trivial $H$-flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non-Abelian T-dual $σ$-models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two-loop order, and it has been concluded that the resulting model is indeed a solution of supergravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $AdS_3 \times S^3$ Background from Poisson-Lie T-Duality Eghbali, Ali High Energy Physics - Theory We proceed to construct a dual pair for the $AdS_3 \times S^3$ background by applying non-Abelian T-duality (here as Poisson-Lie (PL) T-duality on a semi-Abelian double). By using a certain parametrization of the $4$-dimensional Lie group ${A}_2 \otimes 2{A}_1$ and by a suitable choice of spectator-dependent matrices, the original $σ$-model including the $AdS_3 \times S^3$ metric and a non-trivial $B$-field are constructed. The dual background constructed by means of the PL T-duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non-trivial $H$-flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non-Abelian T-dual $σ$-models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two-loop order, and it has been concluded that the resulting model is indeed a solution of supergravity. |
| title | $AdS_3 \times S^3$ Background from Poisson-Lie T-Duality |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.15053 |