Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)dS_d$

TL;DR

This work delivers a fully nonlinear, gauge-invariant framework for symmetric massless higher-spin fields in any dimension by extending Vasiliev's unfolded approach to (A)dS_d. It constructs a star-product based HS algebra from oscillators, introduces a twisted adjoint sector with Weyl 0-forms, and presents a consistent set of nonlinear HS equations that preserve a finite Lorentz subalgebra while incorporating an infinite tower of spins. The Central On-Mass-Shell theorem is recovered at linear order, and perturbative analysis outlines how interactions emerge in a controlled expansion. The formalism admits matrix-valued extensions and various YM groups, suggesting a broad class of interacting HS theories in AdS_d with potential links to string/M-theory and holography.

Abstract

Nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented.