Higher spin holography and the AdS string sigma model

We analyse the cubic spin-3 interaction in AdS space using the higher spin extension of the string-theoretic sigma-model constructed in our previous work, whose low energy limit is described by the AdS vacuum solution. 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 the three-point function of composite operators, quadratic in free fields, in the dual d = 3 vector model. The cancellation of holography violating terms in d = 3 is related to the value of the Liouville background charge in d = 4. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Higher spin theories and holography'. (paper)