More on unconstrained descriptions of higher spin massless particles

Abstract

Here we suggest a new local action describing arbitrary integer spin-s massless particles in terms of only two symmetric fields φ and α 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 α 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 α leads to a unique nonlocal Weyl and diffeomorphism invariant action given only in terms of the physical field φ 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 nonlocal differential operators. We also show that the elimination of α after the Weyl gauge fixing leads to a nonlocal diffeomorphism invariant action previously obtained in the literature.