Higher Spin Symmetries, Star-Product and Relativistic Equations in AdS Space

TL;DR

This work analyzes higher spin gauge theories in $AdS_4$ using star-product (Weyl-oscillator) algebras, linking HS symmetries to AdS geometry and unfolded, covariant formulations. It derives the HS currents and their correspondence to HS gauge fields, constructs the 4D HS algebra with Klein operators, and formulates both free and nonlinear HS dynamics through an unfolded system with auxiliary spinor doubling. The central result is that HS theories are local at linear order but exhibit potential space-time nonlocality at nonlinear order due to higher-derivative interactions, with AdS curvature playing a crucial role in enabling consistent interactions. These insights illuminate the interplay between algebraic structure, geometry, and locality in HS theories and suggest pathways toward non-Abelian and supersymmetric generalizations and potential links to M-theory.

Abstract

We discuss general properties of the theory of higher spin gauge fields in $AdS_4$ focusing on the relationship between the star-product origin of the higher spin symmetries, AdS geometry and the concept of space-time locality. A full list of conserved higher spin currents in the flat space of arbitrary dimension is presented.