Fermionic Solutions of a Five-Dimensional Chern-Simons AdS Supergravity without Gravitino

TL;DR

This paper explores fermionic solutions in a five-dimensional Chern-Simons AdS supergravity model without gravitino, revealing non-linear fermionic equations and conditions for fermion localization through dimensional reduction.

Contribution

It introduces a novel analysis of fermionic solutions in 5D Chern-Simons supergravity without gravitino, using a Randall-Sundrum-type ansatz and uncovering localization properties.

Findings

Derived non-linear fermionic equations of motion.

Identified conditions for fermion chirality localization.

Showed massive fermions coupled to bosonic fields.

Abstract

Based on recent discussions on the so-called unconventional supersymmetry, we analyze a class of solutions of a 5D Chern-Simons AdS-$\mathcal{N}$-SUGRA formulation without gravitino fields. With a Randall-Sundrum-type ansatz, we exploit the properties of Chern-Simons theories to find solutions to the fermionic field equations in a particular dimensional reduction context. We show that this specific dimensional reduction yields a non-trivial equation of motion for the fermionic field. We actually get a non-linear equation of motion for the fermionic fields, typical of models where torsion is present. This fermionic equation describes massive fermions with specific couplings with the bosonic supersymmetric degrees of freedom and we show that, in some specific limits, we can infer about the localization of the fermions' chirality components by means of the particular function that comes out to the dimensional reduction scheme.