  We numerically study optical conductivity $\sigma (\omega )$ near the
"antiferromagnetic" phase transition in the square-lattice Hubbard model at
half filling. We use a cluster dynamical mean field theory and calculate
conductivity including vertex corrections, and to this end, we have
reformulated the vertex corrections in the antiferromagnetic phase. We find
that the vertex corrections change various important details in temperature-
and $\omega$-dependencies of conductivity in the square lattice, and this
contrasts sharply the case of the Mott transition in the frustrated triangular
lattice. Generally, the vertex corrections enhance variations in the
$\omega$-dependence, and sharpen the Drude peak and a high-$\omega$ incoherent
peak in the paramagnetic phase. They also enhance the dip in $\sigma (\omega )$
at $\omega$=0 in the antiferromagnetic phase. Therefore, the dc conductivity is
enhanced in the paramagnetic phase and suppressed in the antiferromagnetic
phase, but this change occurs slightly below the transition temperature. We
also find a temperature region above the transition temperature in which the dc
conductivity shows an insulating behavior but $\sigma (\omega )$ retains the
Drude peak, and this region is stabilized by the vertex corrections. We also
investigate which fluctuations are important in the vertex corrections and
analyze momentum dependence of the vertex function in detail.
