More on dual actions for massive spin-2 particles

Abstract

Here we start from a dual version of Vasiliev’s first order action for massless spin-2 particles (linearized first order Einstein–Hilbert) and derive, via Kaluza–Klein dimensional reduction from D + 1 to D dimensions, a set of dual massive spin-2 models. This set includes the massive ‘BR’ model, a spin-2 analogue of the spin-1 Cremmer–Scherk model. In our approach the linearized Riemann curvature emerges from a solution of a functional constraint. In D = 2 + 1 the BR model can be written as a linearized version of a new bimetric model for massive gravitons. We also have a new massive spin-2 model, in arbitrary dimensions, invariant under linearized diffeomorphisms. It is given in terms of a non symmetric rank-2 tensor and a mixed symmetry tensor.

Hamiltonian analysis and positivity of a new massive spin-2 model

“…On the other hand, integrating over W µν we obtain (after the shift in W µν ) the dual massive spin-2 model proposed in [20] with sources 4…”

“…In [20] a new massive spin-2 model was derived from a massive parent action which in turn was obtained via Kaluza-Klein dimensional reduction of a dual first order version to Vasiliev's action for massless spin-2 particles (linearized first order Einstein-Hilbert) [30]. The new model is invariant under two independent gauge transformations and it can be considered the generalization of the BF action to spin-2.…”

“…where F α = η µβ F [αβ]µ and B = η µν B µν . We have shown in [20] that the equations of motion lead to the Fierz-Pauli [9] conditions and the Klein-Gordon equations…”

“…It is similar to the U(1) invariant Cremmer-Scherk model [21], also called topologically massive BF model in D = 3 + 1, which describes massive spin-1 particles in a gauge invariant way and contains a non Abelian counterpart [22]. The massive model presented in [20] is given in terms of a non-symmetric rank-2 tensor e µν coupled to a mixed symmetry tensor B µ [αβ] similar to a vielbein and a spin connection respectively. The model is invariant under linearized diffeomorphism.…”

Hamiltonian analysis and positivity of a new massive spin-2 model

“…Recently, in [20] we have proposed a new massive spin-2 model dual to the FP theory. It is similar to the U(1) invariant Cremmer-Scherk model [21], also called topologically massive BF model in D = 3 + 1, which describes massive spin-1 particles in a gauge invariant way and contains a non abelian counterpart [22].…”