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.

On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"

“…There is however, no guarantee that no other propagating particles are present. In the four cases s = 1, 3/2, 2, 3, see [1], [21], [12] and [22] respectively, there is a master action connecting L SD 2s−1 with L SD 2s with a D-tensor satisfying (6) and such that L (s)…”