Deficit Angles in 4D Spinfoam with Cosmological Constant: (Anti) de Sitter-ness and More
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914678571008000 |
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| author | Han, Muxin Pan, Qiaoyin |
| author_facet | Han, Muxin Pan, Qiaoyin |
| contents | This paper investigates the critical behaviors of the 4-dimensional spinfoam model with cosmological constant for a general 4-dimensional simplicial complex as the discretization of spacetime. We find that, at the semi-classical regime, the spinfoam amplitude is peaked at the real critical points that correspond to zero deficit angles (modulo $4π\mathbb{Z}/γ$) hinged by internal triangles of the 4-complex. Since the 4-simplices from the model are of constant curvature, the discrete geometry with zero deficit angle manifests a de Sitter (dS) spacetime or an anti de Sitter (AdS) spacetime depending on the sign of the cosmological constant fixed by the boundary condition. The non-(A)dS spacetimes emerge from the complex critical points by an analytic continuation to complex configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deficit Angles in 4D Spinfoam with Cosmological Constant: (Anti) de Sitter-ness and More Han, Muxin Pan, Qiaoyin General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics This paper investigates the critical behaviors of the 4-dimensional spinfoam model with cosmological constant for a general 4-dimensional simplicial complex as the discretization of spacetime. We find that, at the semi-classical regime, the spinfoam amplitude is peaked at the real critical points that correspond to zero deficit angles (modulo $4π\mathbb{Z}/γ$) hinged by internal triangles of the 4-complex. Since the 4-simplices from the model are of constant curvature, the discrete geometry with zero deficit angle manifests a de Sitter (dS) spacetime or an anti de Sitter (AdS) spacetime depending on the sign of the cosmological constant fixed by the boundary condition. The non-(A)dS spacetimes emerge from the complex critical points by an analytic continuation to complex configurations. |
| title | Deficit Angles in 4D Spinfoam with Cosmological Constant: (Anti) de Sitter-ness and More |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2401.14643 |