Higher Spin Holography and AdS String Sigma-Model

We analyze cubic spin 3 interaction in AdS space using the higher spin extension of string-theoretic sigma-model constructed in our previous work, which low energy limit is described by AdS vacuum. We find that, in the leading order of the cosmological constant, the spin 3 correlator on the AdS4 string theory side reproduces the structure of 3 point function of composite operators, quadratic in free fields, in the dual vector model. The cancellation of terms violating higher spin holography is related to the value of the Liouville background charge in four dimensions.