The semiclassical limit of W N CFTs and Vasiliev theory

We propose a renement of the Gaberdiel-Gopakumar duality conjecture be- tween WN conformal eld theories and 2+1-dimensional higher spin gravity. We make an identication of generic representations of the WN CFT in the semiclassical limit with bulk congurations. By studying the spectrum of the semiclassical limit of the WN theories and mapping to solutions of Euclidean Vasiliev gravity at = N, we propose that the 'light states' of the WN 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 elds with these defects. Evidence for this identication comes from comparing charges and from holo- graphic relations between CFT null states and bulk symmetries. We also make progress in understanding the coupling of scalar matter to sl(N) gauge elds.