Asymptotics of $b$-$6j$ symbols and anti-de Sitter tetrahedra
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917105272619008 |
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| author | Liu, Tianyue Ming, Shuang Sun, Xin Wu, Baojun Yang, Tian |
| author_facet | Liu, Tianyue Ming, Shuang Sun, Xin Wu, Baojun Yang, Tian |
| contents | In this paper, we study the asymptotics of the $6j$-symbols for the principal series of the modular double of $\mathrm U_q\mathfrak{sl}(2;\mathbb R)$, and of their analytic extension -- what we call the $b$-$6j$ symbols, relating them in various cases to the volume of truncated hyperideal tetrahedra in the hyperbolic and the anti-de Sitter geometry. To the best of our knowledge, this is the first time that the anti-de Sitter geometry appears in the asymptotics of quantum invariants. In addition, based on the connection to conformal field theory, we reveal a correspondence between the edge lengths and the dihedral angles of truncated hyperideal anti-de Sitter tetrahedra and the Fenchel-Nielsen coordinates of hyperbolic four-holed spheres. We also provide a concrete instance of $3D/2D$ holography, in the spirit of the AdS/CFT correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of $b$-$6j$ symbols and anti-de Sitter tetrahedra Liu, Tianyue Ming, Shuang Sun, Xin Wu, Baojun Yang, Tian Mathematical Physics High Energy Physics - Theory Geometric Topology In this paper, we study the asymptotics of the $6j$-symbols for the principal series of the modular double of $\mathrm U_q\mathfrak{sl}(2;\mathbb R)$, and of their analytic extension -- what we call the $b$-$6j$ symbols, relating them in various cases to the volume of truncated hyperideal tetrahedra in the hyperbolic and the anti-de Sitter geometry. To the best of our knowledge, this is the first time that the anti-de Sitter geometry appears in the asymptotics of quantum invariants. In addition, based on the connection to conformal field theory, we reveal a correspondence between the edge lengths and the dihedral angles of truncated hyperideal anti-de Sitter tetrahedra and the Fenchel-Nielsen coordinates of hyperbolic four-holed spheres. We also provide a concrete instance of $3D/2D$ holography, in the spirit of the AdS/CFT correspondence. |
| title | Asymptotics of $b$-$6j$ symbols and anti-de Sitter tetrahedra |
| topic | Mathematical Physics High Energy Physics - Theory Geometric Topology |
| url | https://arxiv.org/abs/2511.20953 |