Euclidean wormholes for individual 2d CFTs

TL;DR

This work develops a framework to interpret Euclidean wormholes in AdS3 gravity as replica wormholes within individual 2d CFTs, enabling a consistent coarse graining of pure states via wormhole amplitudes. By decohering Virasoro primaries while retaining descendants, the authors show that the Renyi entropies of coarse grained states reproduce wormhole partition functions and relate to horizon areas, extending to multi-copy CFTs and higher-genus boundaries. They further introduce decohered transition matrices and pseudo entropy, providing holographic interpretations in terms of minimal surface areas on wormhole or Euclidean-HRT geometries, and they connect these ideas to island-like entropy and Page curves in a 3d gravity West Coast framework. The results offer a non-ensemble, single-CFT perspective on wormholes, with implications for global charge violation amplitudes and potential future holographic constructions in AdS3/CFT2.

Abstract

We interpret appropriate families of Euclidean wormhole solutions of AdS$_3$ gravity in individual 2d CFTs as replica wormholes described by branching around the time-symmetric apparent horizons of black holes sourced by the backreaction of heavy point particles. These wormholes help describe a rich formalism to coarse grain pure states in 2d CFTs dual to the black hole geometries because the wormhole amplitudes match with the Renyi entropies of CFT states obtained by decohering the pure states in a specific way. This formalism can be generalised to coarse grain pure states in several copies of the dual CFT dual to multi-boundary black holes using wormhole solutions with higher genus boundaries using which we illustrate that coarse graining away the interior of multi-boundary black holes sets the mutual information between any two copies of the dual CFT to zero. Furthermore, this formalism of coarse graining pure states can be extended to decohere transition matrices between pure states which helps interpret more general families of wormhole solutions including those with non replica-symmetric boundary conditions in individual CFTs. The pseudo entropy of the decohered transition matrices has interesting holographic interpretation in terms of the area of minimal surfaces on appropriate black hole or wormhole geometries. The wormhole solutions which show up in the coarse graining formalism also compute the Renyi entropies of Hawking radiation after the Page time in a setup which generalizes the West Coast model to 3d gravity. Using this setup, we discuss the evaporation of one-sided black holes sourced by massive point particles and multi-boundary black holes in 3d gravity.