Holomorphic Factorization at the Quantum Horizon
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929522709889024 |
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| author | Krishnan, Chethan Pathak, Pradipta S. |
| author_facet | Krishnan, Chethan Pathak, Pradipta S. |
| contents | We identify a horizon-skimming limit under which wave equations around large classes of black holes allow a determination of their low-lying (quasi-)degenerate normal modes. Building on our recent work, we use these ``quantum horizon" normal modes to study the thermodynamics of the parent black holes. A key observation is that the UV inputs (the location of the UV regulator, the number of species, and the cut-off in the angular Casimir quantum number) can all be combined into the freedom in a single real parameter. Remarkably, this parameter has an interpretation as the central charge of a holomorphically factorized 2D CFT, and choosing it to be the Kerr-CFT value reproduces the black hole's detailed thermodynamics from the statistical mechanics of normal modes. This perspective provides a heuristic understanding for why the Kerr-CFT central charge is related to the angular momentum of the black hole. The black holes we consider include Kerr-Newman in 3+1 dimensions and Cvetic-Youm in 4+1 dimensions (with all six charges), and they need not be BPS or extremal. Our results show that a refined version of the 't Hooftian quantum gas can be made fully consistent with the thermodynamics of very general black holes. This ``mechanical" approach to the central charge is not directly reliant on asymptotic symmetries in the extremal limit, where the black hole is often unstable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic Factorization at the Quantum Horizon Krishnan, Chethan Pathak, Pradipta S. High Energy Physics - Theory We identify a horizon-skimming limit under which wave equations around large classes of black holes allow a determination of their low-lying (quasi-)degenerate normal modes. Building on our recent work, we use these ``quantum horizon" normal modes to study the thermodynamics of the parent black holes. A key observation is that the UV inputs (the location of the UV regulator, the number of species, and the cut-off in the angular Casimir quantum number) can all be combined into the freedom in a single real parameter. Remarkably, this parameter has an interpretation as the central charge of a holomorphically factorized 2D CFT, and choosing it to be the Kerr-CFT value reproduces the black hole's detailed thermodynamics from the statistical mechanics of normal modes. This perspective provides a heuristic understanding for why the Kerr-CFT central charge is related to the angular momentum of the black hole. The black holes we consider include Kerr-Newman in 3+1 dimensions and Cvetic-Youm in 4+1 dimensions (with all six charges), and they need not be BPS or extremal. Our results show that a refined version of the 't Hooftian quantum gas can be made fully consistent with the thermodynamics of very general black holes. This ``mechanical" approach to the central charge is not directly reliant on asymptotic symmetries in the extremal limit, where the black hole is often unstable. |
| title | Holomorphic Factorization at the Quantum Horizon |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.00732 |