I was watching this https://www.youtube.com/watch?v=Iz2ie3i1Gh0 about Ads/CFT. Very nice video from the master himself. I got confused though about what he calls $N$. Basically he says $N$ is the number of fields and that it should be $N >> 1$ for AdS/CFT to work.

I thought $N$ in this context usually means the number of super symmetries. Is he just being confusing? Sloppy? Or what's going on?


In Maldacena’s original paper two different “n”’s are mentioned in the abstract - $N$ and $\cal{N}$. As Prahar says in the comments, $N$ represents the rank of $SU(N)$ and $\cal{N}$ represents the number of super-symmetries.

Throughout the paper, Maldacena notes that "for large $N$" such and such happens - and, early on in the introduction, "Therefore the solutions can be trusted as long as N is large". This explains the mention of the need for $N >> 1$. Also see section 7 in this for an explanation of the constraints on $N$ and $\cal{N}$.

Hope this helps!


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