More on unconstrained descriptions of Higher Spin Massless Particles

TL;DR

This paper introduces a new local action for arbitrary integer spin-$s$ massless particles using only two symmetric fields, providing an unconstrained, gauge-invariant formulation that reproduces known equations of motion and offers a non-local effective action.

Contribution

It presents a novel unconstrained local action for higher spin massless particles with a Weyl-like symmetry, extending the Fronsdal theory and connecting to string field theory results.

Findings

Derived a local action with two symmetric fields for arbitrary spin-$s$

Showed the equivalence to known equations of motion after gauge fixing

Produced a unique non-local action in the spin-4 case confirming the spectrum

Abstract

Here we suggest a new local action describing arbitrary integer spin-$s$ massless particles in terms of only two symmetric fields $\varphi $ and $\alpha$ of rank-$s$ and $(s-3)$ respectively. It is an unconstrained version of the Fronsdal theory where the double traceless constraint on the physical field is evaded via a rank-$(s-4)$ Weyl like symmetry. The constrained higher spin diffeomorphism is enlarged to full diffeomorphism via the Stueckelberg field $\alpha$ through an appropriate field redefinition. After a partial gauge fixing where the Weyl symmetry is broken while preserving diffeomorphisms, the field equations reproduce, for arbitrary integer spin-$s$, diffeomorphism invariant equations of motion previously obtained via a truncation of the spectrum of the open bosonic string field theory in the tensionless limit. In the $s=4$ case we show that the functional integration over $\alpha$ leads to a unique non local Weyl and diffeomorphism invariant action given only in terms of the physical field $\varphi$ whose spectrum is confirmed via an analysis of the analytic structure of the spin-4 propagator for which we introduce a complete basis of projection and transition non local differential operators. We also show that the elimination of $\alpha$ after the Weyl gauge fixing leads to a non local diffeomorphism invariant action previously obtained in the literature.