The semiclassical limit of W_N CFTs and Vasiliev theory

Abstract

We propose a refinement of the Gaberdiel-Gopakumar duality conjecture between W_N conformal field theories and 2+1-dimensional higher spin gravity. We make an identification of generic representations of the W_N CFT in the semiclassical limit with bulk configurations. By studying the spectrum of the semiclassical limit of the W_N theories and mapping to solutions of Euclidean Vasiliev gravity at \lambda=-N, we propose that the `light states' of the W_N minimal models in the 't Hooft limit map not to the conical defects of the Vasiliev theory, but rather to bound states of perturbative scalar fields with these defects. Evidence for this identification comes from comparing charges and from holographic relations between CFT null states and bulk symmetries. We also make progress in understanding the coupling of scalar matter to sl(N) gauge fields.