Abstract
Here we present the `soldering' of opposite helicity states of a spin-3 particle, in $D=2+1$, into one parity doublet. The starting points may be either the sixth- or the fifth-order (in derivatives) spin-3 self-dual models of opposite helicities. The high number of derivatives avoids the use of auxiliary fields which has been so far an obstacle for a successful soldering procedure. The resulting doublet model is a new Lagrangian with six orders in derivatives and no auxiliary field. It may be regarded as a spin-3 analogue of the linearized `New Massive Gravity'. We check its particle content via a gauge invariant and Lorentz covariant analysis of the analytic structure of the two-point amplitude with the help of spin-3 analogues of the Barnes and Rivers projection operators. The particle content is alternatively confirmed in a specific non-covariant gauge by a decomposition in helicity variables. The soldered model is ghost free and contains two physical states as expected for a parity doublet.
Highlights
Contrary to what happens in D 1⁄4 3 þ 1 dimensions, in the lower dimension D 1⁄4 2 þ 1 it is possible to write down local Lagrangians for elementary spin-s particles with welldefined helicity þs or −s
The high number of derivatives avoids the use of auxiliary fields, which has been so far an obstacle for a successful soldering procedure
Since the two highest order self-dual models SDð63Þ [18] and SDð53Þ [6] only contain one completely symmetric rank-3 tensor without extra fields, which is the minimal tensor structure required for spin-3 particles, they are the best candidates for the soldering procedure
Summary
Contrary to what happens in D 1⁄4 3 þ 1 dimensions, in the lower dimension D 1⁄4 2 þ 1 it is possible to write down local Lagrangians for elementary spin-s particles with welldefined helicity þs or −s. The spin-1 MaxwellProca and the spin-2 Fierz-Pauli models can be obtained via such a procedure just like the spin-3=2 model of [15] Since those doublet Lagrangians have the same form in D 1⁄4 3 þ 1, one can regard the self-dual models in D 1⁄4 2 þ 1 as building blocks of massive particles in D 1⁄4 3 þ 1. Since the two highest order self-dual models SDð63Þ [18] and SDð53Þ [6] only contain one completely symmetric rank-3 tensor without extra fields, which is the minimal tensor structure required for spin-3 particles, they are the best candidates for the soldering procedure. V we reaffirm the self-consistency of the doublet model in terms of helicity variables in a noncovariant gauge
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