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.
Highlights
The so called self-dual models have equivalent equations of motion, such equivalence persists even at the quantum level when we are able in to construct a master action which interpolate among the alternative descriptions
Notice that the MCS model is gauge invariant while the self-dual is not, due to the presence of a Proca mass term. Once such alternative descriptions occurs for particles with higher spins, in the last years we have generalized the proof of equivalence we have observed in the case of spin-1 for spin-2 [3, 4] and spin-3 [5,6] particles in D = 2 + 1
From the statistical point of view we have generalized the NGE approach to the case of fermionic fields, in particular we have analyzed the case of massive spin-3/2 particles, which are described by a vector-spinor field
Summary
The so called self-dual models have equivalent equations of motion, such equivalence persists even at the quantum level when we are able in to construct a master action which interpolate among the alternative descriptions In general they differ each other by an order in derivatives and invariance under gauge transformations. The simplest example we can give refers to the well known equivalence between the self-dual SD [1] and the Maxwell–Chern–Simons models MCS [2] In this case both of them describe a single massive spin-1 particle in D = 2 + 1 dimensions. In this work we have used the Noether Gauge Embedment NGE approach in order to establish the equivalence among self-dual models which describes massive spin-3/2 particles in D = 2 + 1 dimensions. We start the section by verifying the Fierz–Pauli conditions to the vector-spinor, counting the number of degrees of freedom of the first-order self-dual model
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