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.