[Caveat emptor: this is slightly speculative suggestion from a position of relative ignorance.]

There's also another scale in the game in "ordinary" AdS/CFT: while $\lambda$ sets string length, $N$ sets Planck length. Large $N$ suppresses quantum effects, while large $\lambda$ suppresses stringy effects. Stringy (higher derivative) effects have no obvious parallel in Vasiliev, and $\lambda$ has no obvious parallel in the $O(N)$ model. On the other hand, Quantum effects seem like a natural thing to have in the bulk, and $N$ looks rather like the $N$ in SYM. So perhaps the answer is that it's $N$ setting the radius of AdS relative to the Planck length.

Maybe the view of Vasiliev being something like a tensionless, $l_s\to\infty$ limit of strings, with the first Regge trajectory becoming massless, would be a helpful point of view here? I'd need to think a little more to make this feeling any more precise...

This post imported from StackExchange Physics at 2014-03-06 22:07 (UCT), posted by SE-user Holographer