Supersymmetric Chern-Simons vortex systems and fermion zero modes

Fermion zero modes around a general multivortex background are analyzed in supersymmetrized self-dual (Maxwell-) Chern-Simons Higgs systems, using the index theorem and other means. In the models with an $N=2\mathrm{}$ extended supersymmetry, a simple connection is established between all independent fermion zero modes and corresponding bosonic zero modes. We provide a supersymmetry-based explanation of the result.