Let me split the question in a few parts,

Can someone give me a reference which explains the CFT properties of the critical $O(N)$ model in $2+1$? Like how are the CFT correlators (in a $1/N$ expansion?) and the central charge in that calculated?

I guess that by "light" operators one means operators with conformal dimensions smaller than the central charge. Can someone give me a reference which explains as to what are these light states that exist in the critical $O(N)$ model and in what sense are they like a free field? (..as I have often heard being said..)

{..Are there other CFTs out there which have similar properties like the above and do for all of them the central charge grows with some $N$ (the same $N$ in whose large limit the system is having a lot of free-field like light states) ?...}

For any CFT is it true that if it doesn't have "too many" light states then it is probably holographic? (...by "too many" I think it is meant that the number of states (primaries?) with scaling dimensions below the central charge don't grow exponentially in the central charge - may be they can grow at most polynomially?..)

This post imported from StackExchange Physics at 2014-08-11 14:51 (UCT), posted by SE-user user6818