Nonlinear higher spin theories in various dimensions
X. Bekaert, S. Cnockaert, C. Iazeolla, M. A. Vasiliev
TL;DR
The work addresses constructing consistent nonlinear equations for completely symmetric bosonic higher spin fields in AdS spaces across dimensions. It develops an unfolded/free differential algebra framework and builds higher spin algebras from Weyl oscillator algebras, employing star products and twisted adjoint representations to encode dynamics. Central results include the central on-mass-shell and off-mass-shell structure via σ_- cohomology, and the explicit nonlinear Vasiliev-type equations that describe interactions while preserving Sp(2) invariance; perturbative analysis around AdS confirms the correct free-field limit and reveals the structure of higher-order corrections and factorization. The framework offers a robust route toward understanding HS symmetries, their nonlinear dynamics, and potential holographic connections in AdS/CFT contexts, highlighting the role of infinite HS towers and nonlocal interactions in AdS geometries.
Abstract
In this article, an introduction to the nonlinear equations for completely symmetric bosonic higher spin gauge fields in anti de Sitter space of any dimension is provided. To make the presentation self-contained we explain in detail some related issues such as the MacDowell-Mansouri-Stelle-West formulation of gravity, unfolded formulation of dynamical systems in terms of free differential algebras and Young tableaux symmetry properties in terms of Howe dual algebras.