On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915121800937472 |
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| author | Özer, H. T. Filiz, Aytül |
| author_facet | Özer, H. T. Filiz, Aytül |
| contents | This study presents comprehensive examples of $\mathfrak{osp}(\mathcal{N}|2)$ Chern$\,-\,$Simons supergravity on $AdS_3$ for $\mathcal{N}>2$. These formulations, which include the most general boundary conditions, represent extensions of previously discovered works $(\textit{Ozer and Filiz$,$Eur Phys J C 82(5):472, 2022})$ for $\mathcal{N}<3$. In our work, we show that under the loosest set of boundary conditions, the asymptotic symmetry algebras consist of two copies of the $\mathfrak{osp}(3|2)_k$ and $\mathfrak{osp}(4|2)_k$ algebras. We subsequently restrict the gauge fields upon the boundary conditions to achieve supersymmetric extensions of the Brown$\,-\,$Henneaux boundary conditions. Based on these results, we finally find that the asymptotic symmetry algebras are two copies of the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal algebras for $\mathcal{N}=(3,3)$ and $\mathcal{N}=(4,4)$ extended higher$\,-\,$spin supergravity theory in $AdS_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary Özer, H. T. Filiz, Aytül High Energy Physics - Theory This study presents comprehensive examples of $\mathfrak{osp}(\mathcal{N}|2)$ Chern$\,-\,$Simons supergravity on $AdS_3$ for $\mathcal{N}>2$. These formulations, which include the most general boundary conditions, represent extensions of previously discovered works $(\textit{Ozer and Filiz$,$Eur Phys J C 82(5):472, 2022})$ for $\mathcal{N}<3$. In our work, we show that under the loosest set of boundary conditions, the asymptotic symmetry algebras consist of two copies of the $\mathfrak{osp}(3|2)_k$ and $\mathfrak{osp}(4|2)_k$ algebras. We subsequently restrict the gauge fields upon the boundary conditions to achieve supersymmetric extensions of the Brown$\,-\,$Henneaux boundary conditions. Based on these results, we finally find that the asymptotic symmetry algebras are two copies of the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal algebras for $\mathcal{N}=(3,3)$ and $\mathcal{N}=(4,4)$ extended higher$\,-\,$spin supergravity theory in $AdS_3$. |
| title | On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.17235 |