Based on recent discussions on the so-called unconventional supersymmetry, we propose a 5D Chern-Simons AdS-$mathcal{N}$-SUGRA formulation without gravitino fields and show that a residual local SUSY is preserved. We explore the properties of CS theories to find a solution to the field equations in a 5D manifold. With a Randall-Sundrum-type ansatz, we show that this particular dimensional reduction is compatible with SUSY, and some classes of 4D solutions are then analyzed.
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