Coarse graining pure states in AdS/CFT

TL;DR

This paper constructs new Euclidean wormhole solutions in AdS space, interpreting them as overlaps of entangled states from coarse-grained pure states in the dual CFT, and explores their implications for quantum gravity and entropy.

Contribution

It introduces explicit coarse-graining maps in CFT that relate pure states to wormhole geometries, extending previous models to higher dimensions with matter fields.

Findings

Wormholes correspond to overlaps of GHZ-like entangled states.

Coarse-grained entropy equals one quarter the area of an apparent horizon.

Reproduces Page curve and statistical properties of quantum states in higher-dimensional AdS/CFT.

Abstract

We construct new Euclidean wormhole solutions in AdS(d+1) and discuss their role in UV-complete theories, without ensemble averaging. The geometries are interpreted as overlaps of GHZ-like entangled states, which arise naturally from coarse graining the density matrix of a pure state in the dual CFT. In several examples, including thin-shell collapsing black holes and pure black holes with an end-of-the-world brane behind the horizon, the coarse-graining map is found explicitly in CFT terms, and used to define a coarse-grained entropy that is equal to one quarter the area of a time-symmetric apparent horizon. Wormholes are used to derive the coarse-graining map and to study statistical properties of the quantum state. This reproduces aspects of the West Coast model of 2D gravity and the large-c ensemble of 3D gravity, including a Page curve, in a higher-dimensional context with generic matter fields.