  The problems with the $Z_N$ symmetry breaking in the induced QCD are
analyzed. We compute the Wilson loops in the strong coupling phase, but we do
not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to
bypass this problem by adding to the model a heavy fermion field in a
fundamental representation of $ SU(N) $. Remarkably, the model still can be
solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of
flavors. At $ N_f \ll N \rightarrow \infty $ there is a new regime, with two
vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear
integral equation, with the kernel, depending upon the old density. The
symmetry breaking requires certain eigenvalue condition, which takes some extra
parameter adjustment of the scalar potential.
