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

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 nondynamic (spectator) field. The spectator field may be either an antisymmetric tensor B ¼ ÀB , a vector A or a scalar field ', 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 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.

A note on the ubiquity of the traceless spin connection in dual massive spin-2 theories

“…In [20][21][22] we have shown that there are three independent families of second-order models which describe a massive 'spin-2' particle in D dimensions via an arbitrary (nonsymmetric) rank-2 tensor e mn . They can all be written as .…”

“…respectively, the kinetic terms have no particle content, see details in [14]. 4 The connection between Ω μνρ and the metric is made through the 3D identity [19][20][21] one has shown that there are alternative massive spin-2 models to the usual FP theory in D=4 if we assume from the start that e 0 [ ] ¹ mn . In the present work, we replace the starting point (1) by rather general first-order actions which interpolate between those alternative rank-2 models and a dual rank-3 model.…”

Massive spin-2 particles via embedment of the Fierz–Pauli equations of motion

“…Although we use in this work mostly a symmetric tensor = μν νμ h h , it is convenient for the introduction of the embedding idea to recall some results of the works [22,23], where a generic nonsymmetric tensor…”

“…The analytic structure of the propagator of the corresponding free theories is not affected by the extra terms in the action as compared to the usual second order Fierz-Pauli theory. * Although we use in this work mostly a symmetric tensor h µν = h νµ , it is convenient for the introduction of the embedding idea to recall some results of the works [22,23] where a generic nonsymmetric tensor e µν = h µν + B µν , with B µν = −B νµ , is employed. The nonsymmetric FP model (NSFP) is given by 1 1 Throughout this work we use η µν = (−, +, · · · , +).…”

Absence of the Higuchi bound in a family of alternative linear massive spin-2 models

“…In this sense, there is a family of Lagrangians, namely L(a 1 ) [22][23][24], where a 1 is a free parameter, which describes consistently massive spin-2 particles even differing essentially from the FP formulation. Additionally, for a specific value of a 1 , we are led to a ghost-free model that does not contain the paradigmatic FP tuning, by violating the usual idea that it would be the only acceptable mass term.…”