The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime.
Is the converse true? Does any CFT in a suitable number of spacetime dimensions have an AdS/CFT dual? If no, can we characterize the CFTs which have such a dual?
Best Answer
The answer is not known, but many believe it is: "Yes, every CFT has an AdS dual." However, whether the AdS dual is weakly-coupled and has low curvature -- in other words whether it's easy to do calculations with it -- is a different question entirely. We expect, based on well-understood examples (like $\mathcal N=4$ SYM dual to Type IIB strings on $\mathrm{AdS}_5 \times S^5$), that the following is true:
As far as I know, appropriate conditions for CFTs without exactly marginal couplings to have good AdS EFTs are not known. Also, well-understood AdS/CFT dual pairs where the CFT violates one or both of the above conditions are scarce.