Replica Rényi wormholes and generalised modular entropy in JT gravity

A bstract 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 → 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.