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.

15 pages, no figures, typos fixed, massless case revised, 3 references added

References in corpus (6)

• Resummation of Massive Gravity
• Infrared-modified gravities and massive gravitons
• Transverse Fierz-Pauli symmetry
• Non Pauli-Fierz Massive Gravitons
• Dual Massive Gravity
• Duality for massive spin two theories in arbitrary dimensions

Cited by in corpus (5)

• Massive spin-2 particle from a rank-2 tensor
• Massive "spin-2" theories in arbitrary $D\ge 3$ dimensions
• A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields
• A note on higher rank descriptions of massless and massive spin-1 particles
• Absence of the Higuchi bound in a family of alternative linear massive spin-2 models