A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

TL;DR

This paper explores the nonuniqueness of massive spin-2 theories, showing how different models can be related through spectator fields, and discusses implications for massive gravity and higher spin theories.

Contribution

It introduces a method to relate different massive spin-2 models using spectator fields, expanding understanding of their nonuniqueness and potential dual formulations.

Findings

Three independent families of massive spin-2 models identified.

Spectator fields enable interpolation between models.

Fierz-Pauli theory not equivalent to other models with self-interactions.

Abstract

It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. We show here however, that they can be related with the help of a decoupled and non dynamic (spectator) field. The spectator field may be either an antisymmetric tensor $B_{\mu\nu}=-B_{\nu\mu}$, a vector $A_{\mu}$ or a scalar field $\varphi$, corresponding to each of the three families. The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. We argue that massive gravity models based on the Fierz-Pauli theory are not expected to be equivalent to possible local self-interacting theories built up on the top of the two new families of massive spin-2 models. The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher spin particles.