Massive vector Chern-Simons gravity

Abstract

We present a second order gravity action which consists of ordinary Einstein action augmented by a first-order, vector like, Chern-Simons quasi topological term. This theory is ghost-free and propagates a pure spin-2 mode. It is diffeomorphism invariant, although its local Lorentz invariance has been spontaneuosly broken.

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

“…S D [A] may represent the self-dual model of [12] in the spin-1 case or the self-dual models of [7,13] in the spin-2 and spin-3 cases, respectively, while L (2) S D represents the spin-1 Maxwell-Chern-Simons (MC S) model of [14] as well as the second-order models of spin-2 and spin-3 defined in [8,15], respectively. The Lagrangian density L (3) S D stands for both the linearized topologically massive gravity of [14] and the third-order spin-3 model of [9].…”

“…The action (33) is exactly the one for the second-order self-dual model given in [8], except for the source term it automatically includes, the new action for the auxiliary field A μ given by…”

“…In complete analogy with the spin-2 case we have shown that starting with the first-order non-gauge invariant self-dual model [7] it is possible to obtain the second- [8], third- [9] and fourthorder self-dual models, where the last one has all the auxiliary fields needed to correctly describe only one helicity +3 or −3 particle. In [6] we have faced the problem of missing gauge symmetries which are required in order to proceed with the technique and go beyond the fourth-order self-dual model, which might be naively expected since looking at the spin-1 and spin-2 examples, one can see that there are two and four self-dual descriptions for the singlets, respectively, indicating that there might be some 2s rule for the highest order of the spin-s self-dual model, where s is the spin.…”

Gauge invariance and second class constraints in three-dimensional linearized massive gravity

“…These are the selfdual model (SDM) and the so called intermediate model (IM) [10] [11]. The IM corresponds also to the linearization of the curved Vector Chern-Simons gravity action [12]. Both of them have second class constraints.…”

First order actions for new massive dual gravities

“…Also, the general massive gravity [10], the most general gravity theory in three dimensions, propagates two massive gravitons of helicities AE2 but with different masses. Its gauge invariant linearized action was shown to be dual equivalent [11] to the massive spin 2 Fierz-Pauli with a term that breaks explicitly the local Lorentz symmetry [12].…”