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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.16339 |
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| _version_ | 1866929397467971584 |
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| author | Hollowood, Timothy J. Kumar, S. Prem Piper, Luke C. |
| author_facet | Hollowood, Timothy J. Kumar, S. Prem Piper, Luke C. |
| contents | We consider the problem of computing semi-classical Rényi entropies of CFT on AdS$_2$ backgrounds in JT gravity with nongravitating baths, for general replica number $n$. Away from the $n\to 1$ limit, the backreaction of the CFT twist fields on the geometry is nontrivial. For one twist field insertion and general $n$, we show that the quantum extremal surface (QES) condition involves extremisation of the generalised modular entropy, consistent with Dong's generalisation of the Ryu-Takayanagi formula for general $n$. For multiple QES we describe replica wormhole geometries using the theory of Fuchsian uniformisation, explicitly working out the analytically tractable case of the $n=2$ double trumpet wormhole geometry. We determine the off-shell dependence of the gravitational action on the QES locations and boundary map. In a factorisation limit, corresponding to late times, we are able to relate this action functional to area terms given by the value of the JT dilaton at the (off-shell) QES locations, with computable corrections. Applied to the two-sided eternal black hole, we find the $n$-dependent Page times for Rényi enropies in the high temperature limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Replica Rényi Wormholes and Generalised Modular Entropy in JT Gravity Hollowood, Timothy J. Kumar, S. Prem Piper, Luke C. High Energy Physics - Theory General Relativity and Quantum Cosmology We consider the problem of computing semi-classical Rényi entropies of CFT on AdS$_2$ backgrounds in JT gravity with nongravitating baths, for general replica number $n$. Away from the $n\to 1$ limit, the backreaction of the CFT twist fields on the geometry is nontrivial. For one twist field insertion and general $n$, we show that the quantum extremal surface (QES) condition involves extremisation of the generalised modular entropy, consistent with Dong's generalisation of the Ryu-Takayanagi formula for general $n$. For multiple QES we describe replica wormhole geometries using the theory of Fuchsian uniformisation, explicitly working out the analytically tractable case of the $n=2$ double trumpet wormhole geometry. We determine the off-shell dependence of the gravitational action on the QES locations and boundary map. In a factorisation limit, corresponding to late times, we are able to relate this action functional to area terms given by the value of the JT dilaton at the (off-shell) QES locations, with computable corrections. Applied to the two-sided eternal black hole, we find the $n$-dependent Page times for Rényi enropies in the high temperature limit. |
| title | Replica Rényi Wormholes and Generalised Modular Entropy in JT Gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2406.16339 |