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RCFT's (rational conformal field theories) in two dimension are very well-studied, but it seems that there is no any gravity dual of such theories has been found. Is there example of the holographic dual of RCFT?

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Yes, gravity duals have been found for such theories. You can find at least a few examples by picking a particular rational CFT X (,e.g., a minimal model, WZW, Ising) and googling 'AdS dual of X'.

For example:

http://arxiv.org/abs/1011.2986

http://arxiv.org/pdf/1111.1987

http://arxiv.org/abs/1011.5900

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The conjecture on the first paper is incomplete. It suffers the problem on the "light states". There are many states in the W(N) minimal model with dimension of order 1/N, that dosen't have a nice description in the dual theory. I do not want to make any comment on the second paper. The third paper proposed lots of RCFT's that might have gravity duals, but didn't say anything about what those the gravity duals are. – user23875 May 2 at 3:15
I see. Perhaps you could modify your question to indicate what you already know about the literature? – user1504 May 2 at 13:28

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