  We study how the dilepton production rates and electric conductivity are
affected by the phase transition to color superconductivity and the QCD
critical point. Effects of the soft modes associated with these phase
transitions are incorporated through the photon self-energy called the
Aslamazov-Larkin, Maki-Thompson, and density-of-states terms, which are
responsible for the paraconductivity in metallic superconductors. We show that
anomalous enhancements of the production rate in the low energy/momentum region
and the conductivity occur around the respective critical points.
