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

TL;DR

This work introduces the partially broken Fronsdal (PBF) approach for massless higher-spin particles in $D=4$ by enforcing a vanishing double divergence $\partial\cdot\partial\cdot\overline{\Lambda}=0$ on the traceless gauge parameter, thereby reducing gauge symmetry while preserving the irreducible $\pm s$ helicity content for any integer spin $s\ge 3$. The authors develop a gauge-invariant spectrum identification framework, analyze spin-2 and spin-3 cases, and construct a spin-$s$ PBF theory that, after an $r$-shift, decomposes into Fronsdal dynamics plus trace-dependent terms; at special parameter points the theory matches known models (Fronsdal point, SV, Maxwell-like limits) and remains ghost-free. Through both gauge-invariant arguments and light-cone gauge analysis, they prove that the PBF model propagates only the spin-$s$ helicities in $D=4$, with no extra invariants, while enabling broader couplings to sources. The resulting framework generalizes to arbitrary spin with a two-parameter family that reduces to the Fronsdal description at the appropriate limit, offering a simpler irreducible description with potential implications for interactions, curved backgrounds, and tensionless-string limits.

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: $\partial\cdot\partial\cdot\barΛ=0$. 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.