Conformal Coupling of Higher Spin Gauge Fields to a Scalar Field in $AdS_{4}$ and Generalized Weyl Invariance

TL;DR

This paper constructs higher spin interaction currents for a conformally coupled scalar in $AdS_{4}$, exploring their gauge invariance and boundary conditions related to the boundary O(N) sigma model.

Contribution

It provides explicit forms of scalar-gauge field interactions in $AdS_{D}$ and demonstrates their invariance under generalized Weyl transformations.

Findings

Interaction currents are explicitly constructed for both boundary conditions.

Linearized interactions with spin two and four gauge fields are derived.

The work connects bulk higher spin fields with boundary conformal theories.

Abstract

The higher spin interaction currents for the conformally coupled scalar in $AdS_{4}$ space for both regular and irregular boundary condition corresponding to the free and interacting critical point of the boundary O(N) sigma model are constructed. The explicit form of the linearized interaction of the scalar and spin two and four gauge fields in the $AdS_{D}$ space using Noether's procedure for the corresponding spin two and four linearized gauge and generalized Weyl transformations are obtained.