  We present a study of the electrical and thermal conductivities of the
$d$-density wave (DDW) state in an external magnetic field $B$ in the low
temperature regime and in the presence of impurities. We show that in the zero
temperature limit, $T \to 0$, the Wiedemann-Franz (WF) law remains intact. For
finite $T$ the WF law violation is possible and it is enhanced by the external
field.
