Duality and unitarity of massive spin-3/2 models in D= 2 + 1

Abstract

In this work, we provide a triple master action interpolating among three self-dual descriptions of massive spin-3/2 particles in D= 2 + 1 dimensions. Such result generalizes a master action previously suggested in the literature. We also show that, surprisingly a shorthand notation in terms of differential operators applied in the bosonic cases of spins 2 and 3 can also be defined to the fermionic case. With the help of projection operators, we have also obtained the propagator and analyzed unitarity in D dimensions of a second-order spin-3/2 doublet model. Once we demonstrate that this doublet model is free of ghosts, we provide a master action interpolating such model with a fourth-order theory which has several similarities with the spin-2 linearized New Massive Gravity theory.