Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}

TL;DR

This work constructs gauge- and generalized Weyl-invariant, linearized couplings between a conformally coupled scalar and higher-spin fields in $AdS_D$. Using Noether's procedure, it derives a universal tower of currents $Ψ^{(2m)}$ and a gauge-invariant action that couples the scalar to all even spins up to a given spin $ℓ$, with the $ ext{ℓ}=4$ case reproducing known results. It further shows how to extend to a Weyl-invariant action by introducing trace-like corrections $r^{(2m)}$, fixing the Weyl weight Δ$_ℓ$ universally to $1 - D/2$ and determining the accompanying coefficients. The resulting unique linearized action, including all lower-spin towers, provides a robust framework for higher-spin holography and enables tractable calculations of anomalies and loop effects in AdS/CFT contexts.

Abstract

The explicit form of linearized gauge invariant interactions of scalar and general higher even spin fields in the $AdS_{D}$ space is obtained. In the case of general spin $\ell$ a generalized 'Weyl' transformation is proposed and the corresponding 'Weyl' invariant action is constructed. In both cases the invariant actions of the interacting higher even spin gauge field and the scalar field include the whole tower of invariant actions for couplings of the same scalar with all gauge fields of smaller even spin. For the particular value of $\ell=4$ all results are in exact agreement with hep-th/0403241