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I'm beginning to learn AdS/CFT and I have an elementary question. It is said that since it is very hard to calculate 4 point and above correlators in a strongly coupled CFT, we can use instead the AdS/CFT duality to calculate the correlator of the dual field in AdS and take the appropriate boundary limit (that's one way of doing it.)

But we can also use the large $N$ expansion for a strongly coupled field theory. So instead of using the AdS I could directly calculate the correlators in a large $N$ expansion.

So is it that we have 2 different methods for calculating correlators in a strongly coupled field theory? Or are they actually the same method? If they are different, is there a reason to prefer one over the other?

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    $\begingroup$ Can't help but share one of my favourite McGreevy quotes (not talking about AdS/CFT but rather about the Jordan-Wigner transformation): "Possibly Depressing comment. So now you are starting to see that this duality business is actually often a sad story: we thought we could solve two systems (free bosons and free fermions) but since they are really the same system in disguise, it turns out we can only solve one!" Ref: p101 physics.ucsd.edu/~mcgreevy/s14/239a-lectures.pdf $\endgroup$ – Ruben Verresen Jul 29 '16 at 4:37
  • $\begingroup$ large N expansion is for strongly coupled field theories not for specially for conformal field theory.but ADS-CFT will give you correlator for conformal theory.I dont know whether thooft's large N expansion can be formalised to conformal theories also. $\endgroup$ – Hare Krishna Jul 30 '16 at 21:05
  • $\begingroup$ if you use classical gravity in ads then the dual is large N CFT. Specifically 1/N^2 ~ G_N. $\endgroup$ – Nirmalya Kajuri Jul 31 '16 at 14:00
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Strongly coupled refers to the lambda expansion and not the large N.

At large N, you have only planar diagrams, but you can still have large number of vertices weighted by lambda. So, you cant really sum the lambda expansion.

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