Higher spin Lagrangians from higher derivative diffeomorphisms

TL;DR

This paper reveals that higher-spin massless particle actions can be uniquely characterized by invariance under higher-derivative gauge transformations, suggesting a deeper link between higher-spin symmetries and diffeomorphisms.

Contribution

It demonstrates that Fronsdal's higher-spin action is uniquely determined by invariance under higher-derivative gauge transformations, not just standard gauge symmetries.

Findings

Fronsdal's action is uniquely identified by higher-derivative gauge invariance.

Higher-spin gauge transformations can be generalized to higher derivatives.

Potential connection between higher-spin symmetry and diffeomorphisms is suggested.

Abstract

The covariant description of massless particles of arbitrary spin typically employs symmetric tensors of rank $s$ and rests on a local symmetry carried by symmetric tensor parameters of rank $s-1$, suitably generalizing the $U(1)$ transformations of Maxwell's theory and the diffeomorphisms underlying general relativity. Here we show that Fronsdal's action is actually uniquely identified by the weaker requirement of invariance under higher-derivative gauge transformations driven by a vector parameter. This observation may hint to a tighter, if unexpected, connection between higher-spin symmetry and diffeomorphisms.