AdS/CFT at D = 3 AdS/CFT at D = 3 (on the AdS side) seems to have some special issues which I bundled into a single question


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*The CFT is 2D hence it has an infinite-dimensional group of symmetries (locally). The global (Mobius) conformal transformations correspond to isometries of AdS. What is the meaning of the other conformal transformations on the AdS side?

*Is it possible to apply the duality to CFTs with non-zero central charge?

*The CFT can be regarded as a string theory on its own. Hence we get a duality between different string sectors. Is there another way to describe/interpret this duality?

 A: I recommend you Chapter 5 (page 150+) of the AdS Bible,

http://arxiv.org/abs/hep-th/9905111

Concerning your individual questions, which are mostly answered at the beginning of that Chapter,


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*the additional Virasoro generators correspond to bulk coordinate reparametrizations that preserve the metric at infinity, but they do map the ground state to excited states

*yes, the CFTs in AdS/CFT typically have a nonzero central charge which is directly related to the $AdS_3$ curvature radius in the Planck units; there is no reason for $c=0$ here because the boundary CFT isn't really coupled to gravity (which is what the world sheet CFT is doing)

*for the same reason, you can't directly interpret the CFT as string theory; the full string theory needs $c=0$ in total, so extra ghosts must be added; also, the interpretation of "winding/twisted" sectors is different in boundary CFTs and string CFTs. Of course, this doesn't eliminate the fact that similar "building blocks of CFTs" are used in both kinds of CFTs...
