region of $t$. Thus, taking Eq.(\[hhd\]) into account, we obtain that $$\mbox {vacuum configuration}=\left\{\begin{array}{lll}
\mbox{Hosotani phase} &\mbox{for}& \mbar < \mbar_5,\\
\mbox{Higgs phase} & \mbox{for}& \mbar > \mbar_5.
\end{array}\right.
\label{solq}$$ The order parameters are not connected continuously at $\mbar_5$. The phase transition between the two phases is the first order and there is no coexisting phase for this parameter region of $t$.

Collecting all the results obtained above, we depict the phase structure of the model in Fig.2. It should be noted that the Hosotani mechanism, which is usually known to break down gauge symmetry, provides a mechanism of the [*restoration*]{} of the gauge symmetry in the model.

$N=$ even $\geq 4$
------------------

Let us study the case $N=$ even $(\geq 4)$. The type I solution corresponding to the Hosotani phase is given by solving Eq.(\[eqhosotani\]). We obtain, as shown in the appendix, that $${\rm type~~I}~~\cdots~~\left\{\begin{array}{l}
gL\vev{A_y}={\rm diag}\left(\pi, \pi,\cdots,
\pi, -(N-1)\pi\right),\\[0.3cm]
\vev{\Phi}={1\over\sqrt{2}}(0,0,\cdots, 0)^T,
\end{array}\right.
\label{hosotanid}$$ where the phase is stable for the region given by $$0<\mbar < \pi.
\label{regionq}$$ The Wilson line for the configuration (\[hosotanid\]) is $-{\bf 1}_{N\times N}$ and commutes with all the generators of $SU(N)$, so that the $SU(N)$ symmetry is not broken in the phase.

In order 