Lepton flavor violating Z-boson decays at GigaZ as a probe of supersymmetry

We briefly review the lepton flavor violating Z-decays at GigaZ as a probe of supersymmetry by focusing on $Z\to {\mathrm{\ell }}_i{\bar{\mathrm{\ell }}}_j$ in two representative supersymmetric models: the minimal supersymmetric model without R-parity and the supersymmetric seesaw model. We conclude that under the current experimental constraints from LEP and ${\mathrm{\ell }}_i\to {\mathrm{\ell }}_j\gamma$, these rare decays can still be enhanced to reach the sensitivity of the GigaZ. Therefore, supersymmetry can be probed via these decays at GigaZ.