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We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensionsand the existence of extended underlying supersymmetric quantum mechanicsalgebras. Our findings indicate that the fermionic zero modes quantum system inconjunction with the system of zero modes corresponding to bosonicfluctuations, are related to an N=4 extended 1-dimensional supersymmetricalgebra with central charge, a result closely connected to the N=2 spacetimesupersymmetry of the total system. We also add soft supersymmetric terms to thefermionic sector in order to examine how this affects the index of thecorresponding Dirac operator, with the latter characterizing the degeneracy ofthe solitonic solutions. In addition, we analyze the impact of the underlyingsupersymmetric quantum algebras to the zero mode bosonic fluctuations. This isrelevant to the quantum theory of self-dual vortices and particularly for thesymmetries of the metric of the space of vortices solutions and also for thenon-zero mode states of bosonic fluctuations.

Supersymmetric Chern-Simons Vortex Systems and Extended Supersymmetric Quantum Mechanics Algebras