Correlation Functions in Holographic Minimal Models

TL;DR

This paper computes exact correlation functions in holographic minimal models, providing evidence for a 1/N expansion and highlighting the need for additional bulk fields to match boundary correlators.

Contribution

It introduces two methods for computing correlation functions in W_N minimal models and reveals the necessity of extra bulk fields for accurate holographic duality.

Findings

Correlators resemble free-field correlators with 1/N corrections.

Four-point functions are corrected at leading order by additional light operators.

Bulk theory requires modification with extra fields to match boundary correlators.

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.