Massive spin-3/2 models in D = 2 + 1

Abstract

We have demonstrated that the fermionic part of the so called “New Topologically Massive Supergravity”, which is of third order in derivatives, is classically equivalent to self-dual models of lower order in derivatives, forming then a sequence of self-dual descriptions SD(i), with i=1,2,3 meaning the order in derivatives of each description. We have connected all the models by symmetry arguments through a Noether Gauge Embedment approach. This is completely equivalent to what happens in the bosonic cases of spins 1, 2 and 3, so some discussion about the similarities is made along the work. An analogue version of the Fierz–Pauli theory is suggested. Then through the NGE approach a fourth order model is obtained, which in our point of view would be the analogue version of the linearized New Massive Gravity theory for spin-3/2 fermionic particles.