Higher Spin Gauge Theories: Star-Product and AdS Space

TL;DR

The paper investigates higher spin gauge theories in $AdS_3$ and $AdS_4$, focusing on the star-product origin of higher spin symmetries, the structure of HS currents, and explicit solutions to massless equations.It develops both linear (unfolded) and nonlinear HS frameworks, introducing deformed oscillator algebras, extended HS algebras, and free differential algebras to organize an infinite tower of massless fields.A central theme is the tension between space-time locality and the intrinsic nonlocality of star-products, with AdS geometry playing a crucial role in enabling consistent interactions and in shaping the structure of nonlinear corrections.The work also proposes integrating flows to connect nonlinear HS dynamics with free theories, explores d=3 and d=4 realizations, and highlights deep links to string-inspired concepts such as Chan-Paton-type internal symmetries and M-theory.

Abstract

We review the theory of higher spin gauge fields in 2+1 and 3+1 dimensional anti-de Sitter space and present some new results on the structure of higher spin currents and explicit solutions of the massless equations. A previously obtained d=3 integrating flow is generalized to d=4 and is shown to give rise to a perturbative solution of the d=4 nonlinear higher spin equations. A particular attention is paid to the relationship between the star-product origin of the higher spin symmetries, AdS geometry and the concept of space-time locality.