Nonlocality induces isometry and factorisation in holography

In AdS/CFT holography, two manifestations of the black hole information paradox are given by the nonisometric 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 puzzles may be simultaneously resolved by taking into account nonlocal 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 is finite-dimensional with a discrete energy spectrum. The latter gives rise to a transition to a type I von Neumann algebra.