Massive "spin-2" theories in arbitrary $D\ge 3$ dimensions

Abstract

Here we show that in arbitrary dimensions $D\ge 3$ there are two families of second order Lagrangians describing massive "spin-2" particles via a nonsymmetric rank-2 tensor. They differ from the usual Fierz-Pauli theory in general. At zero mass one of the families is Weyl invariant. Such massless theory has no particle content in $D=3$ and gives rise, via master action, to a dual higher order (in derivatives) description of massive spin-2 particles in $D=3$ where both the second and the fourth order terms are Weyl invariant, contrary to the linearized New Massive Gravity. However, only the fourth order term is invariant under arbitrary antisymmetric shifts. Consequently, the antisymmetric part of the tensor $e_{[\mu \nu ]}$ propagates at large momentum as $1/p^2$ instead of $1/p^4$. So, the same kind of obstacle for the renormalizability of the New Massive Gravity reappears in this nonsymmetric higher order description of massive spin-2 particles.

11 pages, 0 figures

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Cited by in corpus (5)

• TDiff and Weyl Invariant Massive Spin-2: Linear Theory
• Massive spin-2 particles in a curved background via a nonsymmetric tensor
• Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor
• Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1
• Absence of the Higuchi bound in a family of alternative linear massive spin-2 models