In a recent discussion at
http://www.nonequilibrium.net/universal-properties-u1-current-deconfined-quantum-critical-points/ ,I became aware of the paper
http://arxiv.org/abs/0806.0110 . Therein, the following statements are proven:
1. AdS/CFT makes a prediction for some quantities c’/c and k’/k, eqn (5).
2. This prediction is compared to the exactly known values for the 3D O(n) model at n = infinity, eqns (28) and (30).
3. The values disagree. Perhaps not by so much, but they are not exactly right.
The standare way of saying this is that the d-dimensional O(n) model does not have a classical gravitational dual, at least not in some neighborhood of n = infinity, d = 3, and hence not for generic n and d. There might be exceptional cases where a gravitational dual exist, e.g. the line d = 2, but generically it seems disproven by the above result. Also note that the O(n) model is one of the most important statphys models, which include the Ising, XY and Heisenberg models for n = 1, 2, 3.
I am on record of being skeptical about the physical relevance of AdS/CFT, but that was mainly because the premises do not seem to hold in nature: physical gravity lives in dS rather than AdS space, and physical QCD is asymptotically free rather than conformal. But the O(n) model at criticality is conformal, so the premises are satisfied, but the result is still wrong. If AdS/CFT does not apply to a CFT with infinitely many components or colors, when can it be trusted? And how do we know if it applies, if we don't have an exact solution to compare to?