  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.
