Higher Spin Gauge Theories in Various Dimensions

TL;DR

Higher spin gauge theories extend gravity to an infinite tower of massless fields in $AdS_d$, requiring non-Abelian HS symmetries and a compensating $o(d-1,2)$-invariant framework. The authors develop an unfolded, star-product-based formulation in which HS fields live in two-row Young-tableau representations and the dynamics are encoded by a noncommutative, covariant system with auxiliary variables, yielding a unique nonlinear theory up to the choice of the spin-1 Yang–Mills group. Central results include the Central On-Mass-Shell Theorem for free HS fields and a complete nonlinear system that preserves HS gauge invariance, albeit at the cost of intrinsic space-time nonlocality and dependence on a nonzero cosmological constant. The work outlines a path to connecting HS theories with string theory via AdS/CFT, while also listing key open problems such as mixed-symmetry fields, action principles, supersymmetric completions, and controlled flat-space limits.

Abstract

Properties of nonlinear higher spin gauge theories of totally symmetric massless higher spin fields in anti-de Sitter space of any dimension are discussed with the emphasize on the general aspects of the approach.