Non-Locality induces Isometry and Factorisation in Holography

TL;DR

This paper demonstrates that non-local quantum corrections, modeled by wormholes, resolve key paradoxes in holography related to black hole information, leading to a finite-dimensional Hilbert space and a transition to a type I von Neumann algebra.

Contribution

It shows that non-local effects from wormholes can simultaneously address the non-isometric bulk-boundary map and factorisation puzzle in holography.

Findings

Hilbert space becomes finite-dimensional with a discrete spectrum

Black hole paradoxes are resolved by wormhole-induced non-local corrections

Transition to a type I von Neumann algebra occurs in the model

Abstract

In holography, two manifestations of the black hole information paradox are given by the non-isometric nature of the bulk-boundary map and by the factorisation puzzle. By considering time-shifted microstates of the eternal black hole, we demonstrate that both these puzzles may be simultaneously resolved by taking into account non-local quantum corrections that correspond to wormholes arising from state averaging. This is achieved by showing, using a resolvent technique, that the resulting Hilbert space for an eternal black hole in Anti-de Sitter space is finite-dimensional with a discrete energy spectrum. The latter gives rise to a transition to a type I von Neumann algebra.