Elements of Vasiliev theory

TL;DR

This paper provides a comprehensive, self-contained overview of Vasiliev higher-spin theories, focusing on their nonlinear equations, and discusses their formulation across various dimensions with detailed background material.

Contribution

It offers a detailed, accessible presentation of Vasiliev equations, including foundational topics like gravity as a gauge theory and free higher-spin fields, with a focus on the four-dimensional case.

Findings

Provides a concise derivation of Vasiliev equations

Includes background on gravity and higher-spin fields

Discusses dimension-independent formulation

Abstract

We propose a self-contained description of Vasiliev higher-spin theories with the emphasis on nonlinear equations. The main sections are supplemented with some additional material, including introduction to gravity as a gauge theory; the review of the Fronsdal formulation of free higher-spin fields; Young diagrams and tensors as well as sections with advanced topics. The shortest route to Vasiliev equations covers 40 pages. The general discussion is dimension independent, while the essence of the Vasiliev formulation is discussed on the base of the four-dimensional higher-spin theory. Three-dimensional and $d$-dimensional higher-spin theories follow the same logic.