An Introduction to Free Higher-Spin Fields

TL;DR

This paper reviews the theoretical framework of free higher-spin fields, including geometric equations, string theory connections, and gauge symmetries, providing a comprehensive overview of the field's foundational concepts.

Contribution

It introduces a local compensator formulation of higher-spin field equations that makes gauge symmetry explicit, extending previous non-local approaches.

Findings

Unified geometric equations for higher-spin fields.

Connection between string theory and higher-spin gauge theories.

A local form of higher-spin equations with explicit gauge symmetry.

Abstract

In this article we begin by reviewing the (Fang-)Fronsdal construction and the non-local geometric equations with unconstrained gauge fields and parameters built by Francia and the senior author from the higher-spin curvatures of de Wit and Freedman. We then turn to the triplet structure of totally symmetric tensors that emerges from free String Field Theory in the $\alpha' \to 0$ limit and to its generalization to (A)dS backgrounds, and conclude with a discussion of a simple local compensator form of the field equations that displays the unconstrained gauge symmetry of the non-local equations. Based on the lectures presented by A. Sagnotti at the First Solvay Workshop on Higher-Spin Gauge Theories held in Brussels on May 12-14, 2004