Coupling of Higher Spin Gauge Fields to a Scalar Field in $Ad{S}_{d+1}$ 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 $\sigma$.

arXiv comment19 pages, Latex

References in corpus (2)

• On the proposed AdS dual of the critical O(N) sigma model for any dimension 2<d<4
• The minimal conformal O(N) vector sigma model at d=3

Cited by in corpus (8)

• Effective action in a higher-spin background
• Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
• Conformal Coupling of Higher Spin Gauge Fields to a Scalar Field in $Ad{S}_4$ and Generalized Weyl Invariance
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• The masses of gauge fields in higher spin field theory on the bulk of $Ad{S}_4$
• The off-shell behaviour of propagators and the Goldstone field in higher spin gauge theory on $Ad{S}_{d+1}$ space
• The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of $Ad{S}_4$
• Lifting a Conformal Field Theory from D-Dimensional Flat Space to (D+1)-Dimensional Ads Space