Report
Replica R\'enyi Wormholes and Generalised Modular Entropy in JT Gravity
| العنوان: | Replica R\'enyi Wormholes and Generalised Modular Entropy in JT Gravity |
|---|---|
| المؤلفون: | Hollowood, Timothy J., Kumar, S. Prem, Piper, Luke C. |
| سنة النشر: | 2024 |
| المجموعة: | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory, General Relativity and Quantum Cosmology |
| الوصف: | We consider the problem of computing semi-classical R\'enyi 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 R\'enyi enropies in the high temperature limit. Comment: 47 pages, 8 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.16339 |
| رقم الانضمام: | edsarx.2406.16339 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |