Cubic Interactions of Bosonic Higher Spin Gauge Fields in $AdS_5$

TL;DR

The paper develops a cubic action for bosonic higher spin fields in $AdS_5$ using a compensator-based gravity framework and an oscillator-based star-product HS algebra built from $su(2,2)$. It formulates the HS degrees of freedom as 1-forms with two-row Young diagram symmetries, establishes the unfolded (Central On-Mass-Shell) description, and derives a bilinear action in curvatures that remains invariant under deformed HS gauge transformations at cubic order. The authors fix the relative couplings across spins by enforcing factorization and a $C$-invariance condition, and demonstrate the existence of consistent cubic HS–gravity interactions in $AdS_5$ (with $S^ ext{ω}=0$) while clarifying the role of the central generator $N$ in producing either infinite copies or reduced spectra. They also discuss reduced models (hu_0 and ho_0) and matrix-extended variants, along with the potential for supersymmetric generalizations and holographic duals to 4d free conformal HS theories. The work provides a concrete,Covariant higher spin framework in five dimensions and lays groundwork for further nonlinear completion and AdS/CFT applications.

Abstract

The dynamics of totally symmetric free massless higher spin fields in $AdS_d$ is reformulated in terms of the compensator formalism for AdS gravity. The $AdS_5$ higher spin algebra is identified with the star product algebra with the $su(2,2)$ vector (i.e., $o(4,2)$ spinor) generating elements. Cubic interactions of the totally symmetric bosonic higher spin gauge fields in $AdS_5$, including the interaction with gravity, are formulated at the action level.