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

TL;DR

This paper analyzes theories of massive spin-2 particles, identifying conditions for ghost-free models and introducing a new family of consistent self-interactions beyond Einsteinian structures.

Contribution

It demonstrates that Einsteinian derivative structures inevitably contain ghosts or lack weak coupling, and introduces a two-parameter family of ghost-free non-Einsteinian cubic self-interactions.

Findings

Einsteinian derivative structures lead to ghosts or non-weakly coupled theories.

Existence of a two-parameter family of ghost-free non-Einsteinian interactions.

Identification of conditions for consistent massive spin-2 theories.

Abstract

We consider general theories of a massive spin-2 particle $h_{\mu\nu}$ on a Minkowski background. A decomposition of $h_{\mu\nu}$ 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 Poincar\'e 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.