Scalar fields and three-point functions in D = 3 higher spin gravity

We compute boundary three-point functions involving two scalars and a gauge field of arbitrary spin in the AdS vacuum of Vasiliev’s higher spin gravity, for any deformation parameter λ. In the process, we develop tools for extracting scalar field equations in arbitrary higher spin backgrounds. We work in the context of hs[λ] ⊕ hs[λ] Chern-Simons theory coupled to scalar fields, and make efficient use of the associative lone-star product underlying the hs[λ] algebra. Our results for the correlators precisely match expectations from CFT; in particular they match those of any CFT with W∞[λ] symmetry at large central charge, and with primary operators dual to the scalar fields. As this is expected to include the ‘t Hooft limit of the WN minimal model CFT, our results serve as further evidence of the conjectured AdS/CFT duality between these two theories.