I have a very generic and naive question on the actual content (and usefulness) of the AdS/CFT conjecture in the low energy approximation where one considers a low energy QFT on AdS, comprising gravity plus a certain number of other fields (e.g. a minimally-coupled scalar with self-interactions)

In this case, it seems to me that the corresponding boundary theory is a crossing symmetric CFT by construction, since:

  • The boundary operators are defined in such a way that their correlation functions automatically satisfy conformal invariance
  • One can derive the OPE in the bulk and apply it to the boundary correlators

I would like to ask what the actual content of the conjecture is in this case, and if it actually adds something to the picture outlined above. Some possibilities I have thought of are:

  • The conjecture is actually meaningful when it relates a given string theory or its low energy limit to a given CFT (such as the original $\mathcal{N}=4$ SYM and type IIB string theory). Related to this, what would then be the usefulness of the correspondence if one does not know what the CFT is?

  • The correspondence actually adds something through the holographic dictionary, e.g. by implying the CFT should have some "large-N-like" expansion corresponding to a weakly coupled gravity dual characterised by an interaction strength $\lambda \propto \frac{1}{N^2}$

  • Consistent theories (i.e. satisfying causality, unitarity etc) on one side have to map onto consistent theories on the other side


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