On ghosts in theories of self-interacting massive spin-2 particles

TL;DR

The work addresses whether nonlinear, local, weakly coupled theories of a massive spin-2 field on Minkowski space can realize a consistent five-degree-of-freedom representation without ghosts. It uses a helicity decomposition of $h_{\mu\nu}$ and a decoupling-limit analysis to compare Einsteinian versus non-Einstein cubic interactions, identifying a ghost problem for Einsteinian cubic vertices and uncovering a two-parameter ghost-free non-Einstein cubic family. Additionally, it derives a general two-derivative cubic action framework that yields a separate ghost-free family with a calculable EFT cutoff, while noting residual tachyonic instabilities. The results constrain viable massive-spin-2 models, clarify the role of derivative structure in ghost formation, and inform EFT considerations and potential phenomenology of massive gravity theories.

Abstract

We consider general theories of a massive spin-2 particle $h_{μν}$ on a Minkowski background. A decomposition of $h_{μν}$ in terms of helicity eigenstates allows us to directly test whether any given theory possesses a consistent description as a massive spin-2 representation of the Poincaré group. We demonstrate (i) that any nonlinear theory with an Einsteinian derivative structure either contains ghosts or does not describe a weakly coupled spin-2 and (ii) that there exists a two-parameter family of non-Einsteinian cubic self-interactions which constitute a ghost-free massive spin-2 theory.