Higher spin AdS$_{3}$ gravity and Tits-Satake diagrams
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916411832532992 |
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| author | Sammani, Rajae Boujakhrout, Youssra Saidi, El Hassan Laamara, Rachid Ahl Drissi, Lalla Btissam |
| author_facet | Sammani, Rajae Boujakhrout, Youssra Saidi, El Hassan Laamara, Rachid Ahl Drissi, Lalla Btissam |
| contents | We investigate higher spin AdS$_{3}$ gravity with real split forms of complex A$_{N}$ B$_{N}$, C$_{N}$ and D$_{N}$ Lie algebras. This is done by linking $SO(1,2)$ spin multiplets with splitted root systems using Tits-Satake diagrams of real forms. Unlike $SL(N,R)$, we show that the orthogonal families have two different higher spin (HS) spectrums: vectorial and spinorial. We find amongst others that the spinorial spectrum has an isolated spin j$_{\mathcal{N}}$ given by $\mathcal{N}\left(\mathcal{N}+1\right)/2$ for $SO(\mathcal{N},1+\mathcal{N})$ and $\mathcal{N} \left( \mathcal{N}-1\right) /2$ for $SO(\mathcal{N},\mathcal{N})$. We implement these results into the computation of the HS partition functions in these gravity theories and identify the individual contributions of the higher spin fields; valuable to manoeuver the HS-BTZ black hole partition function |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher spin AdS$_{3}$ gravity and Tits-Satake diagrams Sammani, Rajae Boujakhrout, Youssra Saidi, El Hassan Laamara, Rachid Ahl Drissi, Lalla Btissam High Energy Physics - Theory We investigate higher spin AdS$_{3}$ gravity with real split forms of complex A$_{N}$ B$_{N}$, C$_{N}$ and D$_{N}$ Lie algebras. This is done by linking $SO(1,2)$ spin multiplets with splitted root systems using Tits-Satake diagrams of real forms. Unlike $SL(N,R)$, we show that the orthogonal families have two different higher spin (HS) spectrums: vectorial and spinorial. We find amongst others that the spinorial spectrum has an isolated spin j$_{\mathcal{N}}$ given by $\mathcal{N}\left(\mathcal{N}+1\right)/2$ for $SO(\mathcal{N},1+\mathcal{N})$ and $\mathcal{N} \left( \mathcal{N}-1\right) /2$ for $SO(\mathcal{N},\mathcal{N})$. We implement these results into the computation of the HS partition functions in these gravity theories and identify the individual contributions of the higher spin fields; valuable to manoeuver the HS-BTZ black hole partition function |
| title | Higher spin AdS$_{3}$ gravity and Tits-Satake diagrams |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.17780 |