Charged CFT observables and AdS/CFT

Question

I have a simple question regarding the holographic dictionary when mapping operators on the CFT side to those in AdS.

One piece of the dictionary is that a global symmetry maps onto a gauge symmetry in the bulk. So if I have operators charged under the global symmetry in the CFT then naively I would assume these are operators charged under the gauge symmetry in the bulk. However, since gauge symmetry is a redundant description we should also restrict to gauge singlet operators, at least to define observables in correlation functions. It seems theres an asymmetry here, all the charged operators on the CFT side are good observables, but only those in the singlet representation map to gauge invariant operators in the bulk.

Is it that the operators in the bulk are also all charged under a global symmetry (assuming we're working in the classical limit on the gravity side so it remains unbroken)?

This post imported from StackExchange Physics at 2015-07-20 09:40 (UTC), posted by SE-user David Meltzer