I have a very basic (and might be very naive) question. What should be the dual gravity description of $N$ (with $N>>1$) free scalars in two dimensions?

I was wondering whether it would be just pure $AdS_3$ because from the seminal work of Brown-Henneaux we know that $$c=\frac{3l}{2G_3}$$and for $N$ free scalars $c=N>>1$ which means $l>>G_3$. So "classical" gravity is good description. In that sense there is no inconsistency. I understand it is very naive argument.

Edit: Here is a related but more concrete question. For $AdS_5/CFT_4$ we know the statement of the conjecture is $\mathcal{N}=4$ SYM in 4D is equivalent to type IIB string theory in $AdS_5 \times S^5$. From there we can take different useful limits (e.g, $l>>l_s$ is SUGRA limit). What is the equivalent statement for $AdS_3/CFT_2$, at least in some 'useful' limit like large central charge etc.?

This post imported from StackExchange Physics at 2015-08-17 08:07 (UTC), posted by SE-user pinu