On the geometry of higher-spin gauge fields

TL;DR

This paper reviews the geometric formulation of free higher-spin gauge fields, their relation to string field theory, and the development of local compensator formulations for unconstrained gauge symmetry.

Contribution

It introduces a geometric approach to higher-spin fields, connecting non-local equations, string theory, and local compensator forms, advancing understanding of unconstrained gauge invariance.

Findings

Unified geometric description of higher-spin fields

Connection between higher-spin geometry and string field theory

Development of local compensator formulations

Abstract

We review a recent construction of the free field equations for totally symmetric tensors and tensor-spinors that exhibits the corresponding linearized geometry. These equations are not local for all spins >2, involve unconstrained fields and gauge parameters, rest on the curvatures introduced long ago by de Wit and Freedman, and reduce to the local (Fang-)Fronsdal form upon partial gauge fixing. We also describe how the higher-spin geometry is realized in free String Field Theory, and how the gauge fixing to the light cone can be effected. Finally, we review the essential features of local compensator forms for the higher-spin bosonic and fermionic equations with the same unconstrained gauge symmetry.