A new constraints separation for the original D=10 massless superparticle

We study the problem of covariant separation between first and second class constraints for the $D=10$ Brink-Schwarz superparticle. Opposite to the supersymmetric light-cone frame separation, we show here that there is a Lorentz covariant way to identify the second class constraints such that, however, supersymmetry is broken. Consequences for the $D=10$ superstring are briefly discussed.Comment: 13 page

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 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 in 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.Comment: 17 pages, no figure

A 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 non dynamic (spectator) field. The spectator field may be either an antisymmetric tensor $B_{\mu\nu}=-B_{\nu\mu}$, a vector $A_{\mu}$ or a scalar field $\varphi$, 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 the 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.Comment: 9 pages, no figure

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

There are three self-dual models of massive particles of helicity +2 (or -2) in $D=2+1$. Each model is of first, second, and third-order in derivatives. Here we derive a new self-dual model of fourth-order, \cL {SD}^{(4)}, which follows from the third-order model (linearized topologically massive gravity) via Noether embedment of the linearized Weyl symmetry. In fact, each self-dual model can be obtained from the previous one \cL {SD}^{(i)} \to \cL {SD}^{(i+1)}, i=1,2,3 by the Noether embedment of an appropriate gauge symmetry, culminating in \cL {SD}^{(4)}. The new model may be identified with the linearized version of \cL {HDTMG} = \epsilon^{\mu\nu\rho} \Gamma_{\mu\gamma}^\epsilon (\p_\nu\Gamma_{\epsilon\rho}^\gamma + (2/3)\Gamma_{\nu\delta}^\gamma \Gamma_{\rho\epsilon}^\delta) /8 m + \sqrt{-g}(R_{\mu\nu} R^{\nu\mu} - 3 R^2/8) /2 m^2 . We also construct a master action relating the third-order self-dual model to \cL {SD}^{(4)} by means of a mixing term with no particle content which assures spectrum equivalence of \cL {SD}^{(4)} to other lower-order self-dual models despite its pure higher derivative nature and the absence of the Einstein-Hilbert action. The relevant degrees of freedom of \cL {SD}^{(4)} are encoded in a rank-two tensor which is symmetric, traceless and transverse due to trivial (non-dynamic) identities, contrary to other spin-2 self-dual models. We also show that the Noether embedment of the Fierz-Pauli theory leads to the new massive gravity of Bergshoeff, Hohm and Townsend.Comment: 14 pages, no figures, typos fixed, reference (19) modifie

Duality of parity doublets of helicity ±2\pm 2 in D=2+1D=2+1

In $D=2+1$ dimensions there are two dual descriptions of parity singlets of helicity $\pm 1$, namely the self-dual model of first-order (in derivatives) and the Maxwell-Chern-Simons theory of second-order. Correspondingly, for helicity $\pm 2$ there are four models $S_{SD\pm}^{(r)}$ describing parity singlets of helicities $\pm 2$. They are of first-, second-,third- and fourth-order ($r=1,2,3,4$) respectively. Here we show that the generalized soldering of the opposite helicity models $S_{SD+}^{(4)}$ and $S_{SD-}^{(4)}$ leads to the linearized form of the new massive gravity suggested by Bergshoeff, Hohm and Townsend (BHT) similarly to the soldering of $S_{SD+}^{(3)}$ and $S_{SD-}^{(3)}$. We argue why in both cases we have the same result. We also find out a triple master action which interpolates between the three dual models: linearized BHT theory, $S_{SD+}^{(3)} + S_{SD-}^{(3)}$ and $S_{SD+}^{(4)} + S_{SD-}^{(4)}$. By comparing gauge invariant correlation functions we deduce dual maps between those models. In particular, we learn how to decompose the field of the linearized BHT theory in helicity eigenstates of the dual models up to gauge transformations.Comment: 15 pages, no figure

Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor

In the last few years we have seen an increase interest on gravitational waves due to recent and striking experimental results confirming Einstein's general relativity once more. From the field theory point of view, gravity describes the propagation of self-interacting massless spin-2 particles. They can be identified with metric perturbations about a given background metric. Since the metric is a symmetric tensor, the massless spin-2 particles present in the Einstein-Hilbert (massless Fierz-Pauli) theory are naturally described by a symmetric rank-2 tensor. However, this is not the only possible consistent massless spin-2 theory at linearized level. In particular, if we add a mass term, a new one parameter $(a_1)$ family of models ${\cal L}(a_1)$ shows up. They consistently describe massive spin-2 particles about Einstein spaces in terms of a non-symmetric rank-2 tensor. Here we investigate the massless version of ${\cal L}(a_1)$ in a curved background. In the case $a_1=-1/12$ we show that the massless spin-2 particles consistently propagate, at linearized level, in maximally symmetric spaces. A similar result is obtained otherwise $(a_1 \ne -1/12)$ where we have a non-symmetric scalar-tensor massless model. The case of partially massless non-symmetric models is also investigated

Generalized duality between local vector theories in D=2+1D=2+1

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in $D=2+1$, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.Comment: 11 pages, no figures, to appear in J. of High Energy Phy

Master actions for massive spin-3 particles in D=2+1

We present here a relationship among massive self-dual models for spin-3 particles in $D=2+1$ via the master action procedure. Starting with a first order model (in derivatives) $S_{SD(1)}$ we have constructed a master action which interpolates among a sequence of four self-dual models $S_{SD(i)}$ where $i=1,2,3,4$. By analyzing the particle content of mixing terms, we give additional arguments that explain why it is apparently impossible to jump from the fourth order model to a higher order model. We have also analyzed similarities and differences between the fourth order $K$-term in the spin-2 case and the analogous fourth order term in the spin-3 context.Comment: 16 page

Dual descriptions of massive spin-3 particles in D=2+1D=2+1 via Noether gauge embedment

We present here a relationship among massive self-dual models for spin-3 particles in $D=2+1$ via the Noether Gauge Embedment $(NGE)$ procedure. Starting with a first order model (in derivatives) $S_{SD(1)}$ we have obtained a sequence of four self-dual models $S_{SD(i)}$ where $i=1,2,3,4$. We demonstrate that the $NGE$ procedure generate the correct action for the auxiliary fields automatically. We obtain the whole action for the $4th$ order self-dual model including all the needed auxiliary fields to get rid of the ghosts of the theory.Comment: 16 pages, 1 tabl