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I am having this very basic problem. In e.g Maldacena's AdS/CFT review (0309246) (page 5), he has defined operators as $\mathcal{O}=N\,{\rm tr}[f(M)]$ for some matrices $M$ and got the connected correlators as $\langle\mathcal{O}\mathcal{O}\rangle_c\sim N^2$ and $\langle\mathcal{O}\mathcal{O}\mathcal{O}\rangle_c\sim N^2$. Whereas in the MAGOO review (9905111) (page 14-15 e.g) we see some operators defined as $G$ which is added to the action as $S\rightarrow S+N\sum g_jG_j$ which gives the correlators as $\langle\prod_j G_j\rangle\sim N^{2-n}$. So that three points and higher vanish at large N. I thought this one is generic. If so I wanted to understand how is the first conventions/case are different and their difference (has it something to do with connected/disconnected diagram? etc.).

Related to that I wanted to know about large N factorization. For a particular model if I calculate disconnected diagrams, I see that at large N I indeed get this factorization. I learned that its like WKB in $\hbar\sim 1/N$. But I wanted to feel it more generally in possibly a mathematical+insightful way if possible.

Thanks for the help.

Edit: If it has a long answer please at least let me know which way to think or any references where I can get some ideas. Thanks again.

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