Nonlinear higher spin theories in various dimensions

TL;DR

This paper introduces nonlinear equations for symmetric bosonic higher spin gauge fields in anti de Sitter space across various dimensions, covering foundational formulations and algebraic structures.

Contribution

It provides a comprehensive, self-contained overview of nonlinear higher spin theories, including detailed explanations of related formalisms and algebraic tools.

Findings

Formulation of nonlinear higher spin equations in AdS space

Explanation of unfolded formulation and free differential algebras

Analysis of Young tableaux and Howe dual algebras

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.