Eternal Black Holes and Superselection in AdS/CFT

TL;DR

This paper argues that in AdS/CFT, superselection sectors are necessary to distinguish different wormhole connections between black holes, which cannot be identified with separate entangled CFTs, affecting the understanding of bulk quantum states.

Contribution

It demonstrates that superselection sectors labeled by wormhole types are essential in AdS/CFT, challenging previous identifications of entangled states with separate bulk systems.

Findings

Superselection sectors are necessary for different wormhole connections.

Dual CFTs cannot distinguish these superselection sectors.

Restrictions relate to spin-statistics and black hole configurations.

Abstract

It has been argued i) that Lorentz-signature solutions with wormholes connecting n asymptotically AdS regions describe bulk quantum states dual to n entangled but non-interacting CFTs and ii) that such bulk wormhole states should be identified with similar entangled but non-interacting bulk systems, each describing quantum geometries with only a single asymptotic region. But if the wormhole is to behave semiclassically, we show that conjecture (ii) cannot hold. Instead, the theory of asymptotically AdS bulk quantum gravity must admit superselection sectors with respect to the CFT observables that are labeled by the type of wormhole connections allowed between black holes. Moreover, these superselection sectors are indistinguishable in the dual CFT. Finally, we describe restrictions on the possible superselection sectors associated with the spin-statistics relation and the expectation that black holes lying in distinct asymptotically AdS regions may be approximated by well-separated black holes in a single asymptotically AdS region.