Cusps in 3d gravity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918166665363456 |
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| author | Stanford, Douglas Yan, Cynthia |
| author_facet | Stanford, Douglas Yan, Cynthia |
| contents | Three dimensional hyperbolic manifolds have accumulation points in the spectrum of their volumes, leading to a divergence in the sum over topologies. The limit points are cusped hyperbolic manifolds, and we propose to renormalize the sum by including the cusped manifold as a counterterm. This gives a reinterpretation of the zeta-function regularization procedure used by Maloney and Witten in the sum over SL(2,Z) black holes. For pure N = 1 supergravity, cusps with even spin structure can be used in a similar way. Cusps with odd spin structure are not needed to cancel any divergence, but they find an application by making the index nonzero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cusps in 3d gravity Stanford, Douglas Yan, Cynthia High Energy Physics - Theory General Relativity and Quantum Cosmology Three dimensional hyperbolic manifolds have accumulation points in the spectrum of their volumes, leading to a divergence in the sum over topologies. The limit points are cusped hyperbolic manifolds, and we propose to renormalize the sum by including the cusped manifold as a counterterm. This gives a reinterpretation of the zeta-function regularization procedure used by Maloney and Witten in the sum over SL(2,Z) black holes. For pure N = 1 supergravity, cusps with even spin structure can be used in a similar way. Cusps with odd spin structure are not needed to cancel any divergence, but they find an application by making the index nonzero. |
| title | Cusps in 3d gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.19920 |