Speaker
Description
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 have demonstrated 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. Moreover, I will discuss how geometric phases may be used to describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of their Hilbert space. We find a direct relation between geometric phases and von Neumann algebras, and show that a vanishing geometric phase implies the existence of a well-defined trace functional on the algebra. We discuss how this is realised within the AdS/CFT correspondence for the eternal black hole.