Coupling of Higher Spin Gauge Fields to a Scalar Field in $AdS_{d+1}$ and their Holographic Images in the $d$-Dimensional Sigma Model

Abstract

The three-point functions of two scalar fields $\sigma$ and the higher spin field $h^{(\ell)}$ of HS(4) on the one side and of their proposed holographic images $\alpha$ and $\mathcal{J^{(\ell)}}$ of the minimal conformal O(N) sigma model of dimension three on the other side are evaluated at leading perturbative order and compared in order to fix the coupling constant of HS(4). This necessitates a careful analysis of the local current $\Psi^{(\ell)}$ to which $h^{(\ell)}$ couples in HS(4) and which is bilinear in $\sigma$.