Massive deformations of rank-2 symmetric tensor theory (a.k.a. BRS characterization of Fierz-Pauli massive gravity)

TL;DR

This paper explores the space of massive deformations of symmetric rank-2 tensor gauge theories, identifying conditions for ghost-free models and highlighting the unique role of Fierz-Pauli massive gravity via BRS symmetry.

Contribution

It characterizes all possible ghost-free massive deformations of rank-2 tensor gauge theories and demonstrates the unique identification of Fierz-Pauli gravity through BRS cohomology.

Findings

Multiple ghost-free massive theories identified

Fierz-Pauli mass term distinguished by BRS symmetry

Several models with good massless limits found

Abstract

In this paper we consider the issue of massive gravity from a pure field theoretical point of view, as the massive deformation of the gauge theory for a symmetric rank-2 tensor field. We look for the most general massive theory with well defined propagators, imposing the absence of unphysical poles (ghosts). We find several possibilities, depending on the choice of the gauge fixing term. {Amongst these, two solutions with good massless limit are found.} The request of the absence of ghosts, alone, does not isolate the Fierz-Pauli case: several examples of massive theories, which may include or not the Fierz-Pauli mass term, are given. On the other hand, the Fierz-Pauli theory can be uniquely identified by means of a symmetry: it turns out the the Fierz-Pauli massive gravity is the only element of the cohomology of a BRS operator.