We construct a simple class of exact solutions of the electroweak theory
including the naked Z--string and fermion fields. It consists in the
Z--string configuration (ϕ,Zθ), the {\it time} and z components
of the neutral gauge bosons (Z0,3,A0,3) and a fermion condensate
(lepton or quark) zero mode. The Z--string is not altered (no feed back from
the rest of fields on the Z--string) while fermion condensates are zero modes
of the Dirac equation in the presence of the Z--string background (no feed
back from the {\it time} and z components of the neutral gauge bosons on the
fermion fields). For the case of the n--vortex Z--string the number of zero
modes found for charged leptons and quarks is (according to previous results by
Jackiw and Rossi) equal to ∣n∣, while for (massless) neutrinos is ∣n∣−1.
The presence of fermion fields in its core make the obtained configuration a
superconducting string, but their presence (as well as that of
Z0,3,A0,3) does not enhance the stability of the Z--string.Comment: 12 text pages (Latex) and 8 postscript figures in a uuencoded fil