Three-Point Functions in N=2 Higher-Spin Holography

Abstract

The CP^N Kazama-Suzuki models with the non-linear chiral algebra SW_infinity[lambda] have been conjectured to be dual to the fully supersymmetric Prokushkin-Vasiliev theory of higher-spin gauge fields coupled to two massive N=2 multiplets on AdS_3. We perform a non-trivial check of this duality by computing three-point functions containing one higher-spin gauge field for arbitrary spin s and deformation parameter lambda from the bulk theory, and from the boundary using a free ghost system based on the linear sw_infinity[lambda] algebra. We find an exact match between the two computations. In the 't Hooft limit, the three-point functions only depend on the wedge subalgebra shs[lambda] and the results are equivalent for any theory with such a subalgebra. In the process we also find the emergence of N=2 superconformal symmetry near the AdS_3 boundary by computing holographic OPE's, consistently with a recent analysis of asymptotic symmetries of higher-spin supergravity.