Correlation Functions in Holographic Minimal Models

Abstract

We compute exact three and four point functions in the W_N minimal models that were recently conjectured to be dual to a higher spin theory in AdS_3. 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 1/N expansion since our correlators look like free-field correlators corrected by a power series in 1/N . However, on examining these corrections we find that the four point function of the two bulk scalar fields is corrected at leading order in 1/N 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.