Linear connections with propagating spin-3 field in gravity

TL;DR

This paper demonstrates that a free massless spin-3 gauge field's Lagrangian can be embedded within a metric-affine gravity framework, revealing geometric structures and exact solutions with propagating spin-3 fields.

Contribution

It shows how Fronsdal's Lagrangian for spin-3 fields is contained in a Yang--Mills-like metric-affine gravity theory, linking higher-spin fields with geometric gauge theories.

Findings

Embedding of spin-3 Lagrangian in MAG framework

Construction of exact solutions with propagating spin-3 fields

Identification of spin-3 frame with nonmetricity tracefree form

Abstract

We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime is contained in a general Yang--Mills-like Lagrangian of metric-affine gravity (MAG), the gauge theory of the general affine group in the presence of a metric. Due to the geometric character of MAG, this can best be seen by using Vasiliev's frame formalism for higher-spin gauge fields in which the spin-3 frame is identified with the tracefree nonmetricity one-form associated with the shear generators of GL(n,R). Furthermore, for specific gravitational gauge models in the framework of full nonlinear MAG, exact solutions are constructed, featuring propagating massless and massive spin-3 fields.