Unitarity of partially broken massless higher-spin models

Abstract

Here we suggest a partially broken version of the Skvortsov-Vasiliev (SV) model for massless particles of arbitrary integer spin $s\ge 3$. The traceless gauge parameter of the Weyl transformation is now required to be transverse. In the light-cone gauge we offer a simple proof that the model contains only spin-$s$ helicities as propagating modes. In the $s=3$ and $s=4$ cases we are able to calculate the two point amplitude and confirm unitarity in a explicitly Lorentz invariant way. For the recently suggested partially broken Fronsdal model, for $s=3$ and $s=4$, unitarity is also confirmed in a Lorentz invariant way from their two point amplitudes. In both Fronsdal and SV partially broken models the two point amplitudes differ from their unbroken counterparts by contact terms which guarantees the same particle content but indicates potential non-equivalence of possible interacting terms.