Higher Spin Gauge Theories in Any Dimension

TL;DR

This paper argues that consistent nonlinear higher spin gauge theories can be formulated in any dimension by embedding HS fields into a gauge connection of a higher-spin algebra and describing dynamics in an unfolded, star-product framework. The construction relies on doubling auxiliary variables and employing a noncommutative fiber space to generate interactions, with AdS geometry and its radius playing a pivotal role in enabling higher-derivative couplings. Central results include the central on-mass-shell theorem, the nonlinear Vasiliev-type equations, and the realization of singletons that organize the HS spectrum, including fermions and mixed-symmetry fields. The framework strengthens the link between HS theories, AdS/CFT, and string theory, offering a concrete, gauge-consistent pathway to explore holographic duals and high-energy symmetries beyond conventional field theories.

Abstract

Some general properties of higher spin gauge theories are summarized with the emphasize on the nonlinear theories in any dimension.