Correlation functions in holographic minimal models

We compute exact three- and four-point functions in the WN minimal models that were recently conjectured to be dual to a higher spin theory in AdS3. The boundary theory has a large number of light operators that are not only invisible in the bulk but grow exponentially with N even at small conformal dimensions. Nevertheless, we provide evidence that this theory can be understood in a 1N expansion since our correlators look like free-field correlators corrected by a power series in 1N. However, on examining these corrections we find that the four-point function of the two bulk scalar fields is corrected at leading order in 1N through the contribution of one of the additional light operators in an OPE channel. This suggests that, to correctly reproduce even tree-level correlators on the boundary, the bulk theory needs to be modified by the inclusion of additional fields. As a technical by-product of our analysis, we describe two separate methods-including a Coulomb gas type free-field formalism-that may be used to compute correlation functions in this theory.