Abstract
The soldering procedure has been for the first time generalized to the case of spin-3/2 fermionic theories. We have demonstrated that the fermionic part of the so-called “New Topologically Massive Supergravity” theory, which is of third order in derivatives, can be soldered in order to obtain a fourth order doublet model analogue to the linearized version of the New Massive Gravity theory, while the soldering of two second order self-dual models give us a theory similar to the linearized version of the Einstein–Hilbert–Fierz–Pauli theory.
Highlights
In D = 2 + 1 dimensions self-dual models describes massive particles with spin +s or −s
We have studied in [1] the connection among three massive spin-3/2 self-dual versions of first, second and third order in derivatives through symmetry arguments
We have considered an analogue version of the Proca theory which is second order in derivatives and which by means of the Fierz–Pauli conditions describes correctly two massive propagating modes of helicities +3/2 and −3/2. This doublet model1 is by its turn connected to a fourth order doublet model which we believe is free of ghosts
Summary
We have considered an analogue version of the Proca (or Fierz–Pauli) theory which is second order in derivatives and which by means of the Fierz–Pauli conditions describes correctly two massive propagating modes of helicities +3/2 and −3/2 This doublet model is by its turn connected to a fourth order doublet model which we believe is free of ghosts. The procedure can be extended to the soldering of third and fourth order self-dual models, the result in both cases are the same, the linearized version of the N MG theory [10]. Is an original attempt to try the soldering of fermionic models which do not demand the presence of auxiliary fields This is precisely the case of the massive spin-3/2 theories. The doublet models we have obtained here can be interpreted as analogue versions of the MC S-Proca model or in other case as the linearized version of the N MG theory
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