The semiclassical limit of W_N CFTs and Vasiliev theory

Understand

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.