  We study two fermionic systems that have an underlying supersymmetric
structure, namely a color superconductor and Dirac fermion in a
Reissner-Nordstr\"{o}m-anti-de Sitter gravitational background. In the chiral
limit of the color superconductor, the localized fermionic zero modes around
the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all
the operators being Fredholm. We compute the Witten index of this algebra and
we find an unbroken supersymmetry. The fermionic gravitational system in the
chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric
algebras. The unbroken supersymmetry in the later is guaranteed by the
existence of fermionic quasinormal modes in the Reissner-Nordstr\"{o}m-anti-de
Sitter background. In this case the operators are not Fredholm and regularized
indices are deployed.
