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

Abstract

We present here a relationship among massive self-dual models for spin-3 particles in D = 2 + 1 via the Noether Gauge Embedment (N GE) 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 N GE 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.

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

“…We find an alternative explanation of why it is apparently impossible to complete the chain of 2s models in the spin-3 case, and give a demonstration that the classical equivalence between first-, second-, third-and fourth-order spin-3 models obtained in [6] holds also at the quantum level.…”

“…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]. Finally L (4) S D may represent either the linearized version of the higher derivative topologically massive gravity of [5,16] or the spin-3 fourth-order model whose main equations of motion are given in [10] and the whole action in [6]. More precisely, the A-field in (1) stands for a rank-s tensor field and in the spin-s case while L…”

“…The Fierz-Pauli conditions can be obtained from the equations of motion derived from (22), demonstrations can be found in [6,7]. By adding mixing terms without particle content we aim to construct a master action from (22).…”

“…Recently, we have addressed [6] this subject through another dualization procedure, the Noether Gauge Embedding, NGE, which is based on the existence of a local symmetry in the highest derivative term of the self-dual model which is not present in the lower derivative terms. 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 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. In fact the authors in [10] have proposed fifth-and sixth-order equations of motion, for a massive spin-3 particle, however, without considering auxiliary fields, where, however, the fifth-order model contains ghosts.…”