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Replica Rényi wormholes and generalised modular entropy in JT gravity

Timothy Hollowood Orcid Logo, Prem Kumar Orcid Logo, Luke Piper

Journal of High Energy Physics, Volume: 2024

Swansea University Authors: Timothy Hollowood Orcid Logo, Prem Kumar Orcid Logo, Luke Piper

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DOI (Published version): 10.1007/jhep10(2024)169

Abstract

We consider the problem of computing semi-classical Rényi entropies of CFTon AdS2 backgrounds in JT gravity with nongravitating baths, for general replica number n. Away from the n =1 limit, the backreaction of the CFT twist fields on the geometry is nontrivial. For one twist field insertion and gen...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Nature 2024
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa68052
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Abstract: We consider the problem of computing semi-classical Rényi entropies of CFTon AdS2 backgrounds in JT gravity with nongravitating baths, for general replica number n. Away from the n =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 andboundary 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.
Keywords: 2D Gravity, Black Holes
College: Faculty of Science and Engineering
Funders: TJH and SPK would like to acknowledge support from STFC Consolidated Grant Award ST/X000648/1. LCP is supported by a joint STFC studentship ST/V507143/1 and EPSRC DTP, Faculty of Science & Engg, Swansea U. SPK would like to thank the Fields, Gravity & Strings group, Laboratoire de Physique de L’ École Normale Supérieure for hospitality whilst this work was being completed.

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