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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fierz-Pauli higher derivative gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. We show here, however, that they can be related with the help of a decoupled and nondynamic (spectator) field. The spectator field may be either an antisymmetric tensor B μν=-Bνμ, a vector Aμ or a scalar field φ, corresponding to each of the three families. The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. We argue that massive gravity models based on the Fierz-Pauli theory are not expected to be equivalent to possible local self-interacting theories built up on top of the two new families of massive spin-2 models. The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher-spin particles. © 2013 American Physical Society.

Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new spin-2 self-dual model in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dual descriptions of spin-two massive particles in D=2+1 via master actions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Unavoidable conflict between massive gravity models and massive topological terms

Massive gravity models in (2 + 1) dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar squared (R-2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern-Simons term. Furthermore, if the massive topological term is added to R + R-munu(2) gravity, or to R + R-munu(2), + R-2 gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.

Generalized soldering of +/- 2 helicity states in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Note on linearized new massive gravity in arbitrary dimensions

By means of a triple master action we deduce here a linearized version of the new massive gravity (NMG) in arbitrary dimensions. The theory contains a 4th-order and a 2nd-order term in derivatives. The 4th-order term is invariant under a generalized Weyl symmetry. The action is formulated in terms of a traceless ημνΩμνρ=0 mixed symmetry tensor Ωμνρ=-Ωμρν and corresponds to the massive Fierz-Pauli action with the replacement e μν=∂ρΩμνρ. The linearized 3D and 4D NMG theories are recovered via the invertible maps Ωμνρ=Ïμνρβhβμ and Ωμνρ=ÏμνργδT [γδ]μ respectively. The properties h μν=hνμ and T[[γδ]μ]= 0 follow from the traceless restriction. The equations of motion of the linearized NMG theory can be written as zero curvature conditions ∂νTρμ-∂ρT νμ=0 in arbitrary dimensions. © 2013 American Physical Society.

Massive spin-2 particle from a rank-2 tensor

Here we obtain all possible second-order theories for a rank-2 tensor which describe a massive spin-2 particle. We start with a general second-order Lagrangian with ten real parameters. The absence of lower-spin modes and the existence of two local field redefinitions leads us to only one free parameter. The solutions are split into three one-parameter classes according to the local symmetries of the massless limit. In the class which contains the usual massive Fierz-Pauli theory, the subset of spin-1 massless symmetries is maximal. In another class where the subset of spin-0 symmetries is maximal, the massless theory is invariant under Weyl transformations and the mass term does not need to fit into the form of the Fierz-Pauli mass term. In the remaining third class neither the spin-1 nor the spin-0 symmetry is maximal and we have a new family of spin-2 massive theories. © 2013 American Physical Society.

Massive spin-2 theories in arbitrary D>= 3 dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

A note on spin-s duality

Duality is investigated for higher spin (s ≥ 2), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D = 4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s = 2) or Fronsdal (s ≥ 3) action (as it is the case for spin 1). In the particular s = 2 D = 5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev. © SISSA/ISAS 2003.