Pseudo-Linear Spin-2 Interactions

Abstract

We show how the pseudo-linear interactions for spin-2 particles can be straightforwardly extended to include multiple massive and massless fields without introducing ghosts. When massive spin-2 fields are included, these give simple analogues of bi-gravity and multi-gravity theories with mass terms that break linear gauge symmetries. The interactions containing only massless particles cannot be written in terms of linearized curvature tensors and are gauge invariant only up to a total derivative. These correspond to known theories that exist in more than four dimensions and evade the no-go results on interacting massless spin-2 particles.