Nonuniqueness of the Fierz-Pauli mass term for a nonsymmetic tensor

Abstract

Starting with a description of massive spin-2 particles in D=4 in terms of a mixed symmetry tensor \(\tmnd \) without totally antisymmetric part (\(T_{[[\mu\nu]\rho]}=0\)) we obtain a dual model in terms of a nonsymmetric tensor \(e_{\mu\nu}\). The model is of second-order in derivatives and its mass term \((e_{\mu\nu}e^{\nu\mu} + c \, e^2)\) contains an arbitrary real parameter \(c\). Remarkably, it is free of ghosts for any real value of \(c\) and describes a massive spin-2 particle as expected from duality. The antisymmetric part \(e_{[\mu\nu]}\) plays the role of auxiliary fields, vanishing on shell. In the massless case the model describes a massless spin-2 particle without ghosts.