Geometric Second Order Field Equations for General Tensor Gauge Fields

TL;DR

This paper develops geometric second order field equations for higher spin tensor gauge fields, extending previous work to all Lorentz group representations, with non-local actions that become local under gauge fixing or auxiliary fields.

Contribution

It introduces geometric second order equations for higher spin bosons and first order for fermions, generalizing Francia and Sagnotti's results to all Lorentz group representations.

Findings

Constructed second order gauge-invariant equations for higher spin bosons.

Formulated first order equations for higher spin fermions.

Provided non-local actions that become local with gauge fixing or auxiliary fields.

Abstract

Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.