Unitarity of partially broken massless higher-spin models

TL;DR

This work constructs and analyzes partially broken higher-spin models, PBSV and PBF, for massless bosonic fields with spin $s \ge 3$. It shows that PBSV shares the same particle content as SV, while the reduced gauge symmetry constrains trace components via a rank-$(s-3)$ condition, and validates this in the light-cone gauge and via Lorentz-invariant two-point amplitudes. For spins $s=3,4$, the Lorentz-invariant two-point amplitudes confirm unitarity and reveal that PBSV and PBF differ from their unbroken counterparts only by contact terms, implying identical propagating content but potential differences in interacting terms. The results indicate no strong duality at the level of action-level dualities between broken and unbroken formulations, motivating further study of consistent interactions in these partially broken higher-spin theories.

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.