A partially broken Fronsdal model for massless higher-spin particles of integer spin

TL;DR

This paper introduces a modified Fronsdal model with arbitrary parameters that still describes massless particles of any integer spin, revealing a broader gauge symmetry constraint without extra propagating invariants.

Contribution

It identifies a new region in parameter space of the Fronsdal model where massless higher-spin particles are described with a modified gauge symmetry constraint.

Findings

The model describes only spin-$s$ helicity states as propagating modes.

The gauge symmetry is constrained by a double divergence condition on the gauge parameter.

More general source couplings are possible compared to the original Fronsdal model.

Abstract

By introducing arbitrary parameters in the usual Fronsdal model, we find a region in the parameters space away from the ``Fronsdal point'' where we still have an irreducible description of massless particles of arbitrary integer spin $s\ge 3$. The higher spin gauge symmetry is further constrained by a vanishing double divergence condition on the traceless gauge parameter: $\partial\cdot\partial\cdot\bar\Lambda=0$. Remarkably, it does not introduce extra propagating gauge invariants. We demonstrate that we only have spin-$s$ helicity states as propagating modes for arbitrary integer $s\ge 3$. For the simplest $s=3$ case we present a gauge invariant proof while for $s\ge 4$ we use a light-cone gauge. The reduction in the gauge symmetry allows for more general source couplings when compared to the Fronsdal model.