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Main Authors: Hollowood, Timothy J., Kumar, S. Prem, Piper, Luke C.
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2406.16339
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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