Abstract
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.
Highlights
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 [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
Summary
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 the master action approach a fundamental ingredient consists of finding appropriate mixing terms between the dual fields, which cannot have by themselves any particle content when diagonalized. We propose a master action that interpolates between the first three spin-3 selfdual models, and obtain their dual maps. As a last step we show that is possible to construct a new master action using only totally symmetric fields, which interpolates between the third and the fourth-order self-dual models. In the last section final remarks on the particle content of the fourth-order term clarify the difficulties in going beyond the fourth-order selfdual model
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