\end{array}\right),
\end{split}$$ where the first line contains the Gell-Mann matrices $\lambda_a$, the generators of the unbroken $SU(3)$ and $T_{15}$ the generator of the unbroken $U(1)$. The Wilson line phase can be written $U=e^{i\beta^aT_a}$ as in Eq. \[eq:uso3\] and it must comply with the consistency condition from Eq. \[eq:pupu\] $$1=P_MUP_MU=P_M e^{i\beta^aT_a}P_Me^{i\beta^aT_a}=e^{i\beta^a(P_MT_aP_M)}e^{i\beta^aT_a}.$$ It can easily be seen that $$\begin{split}
P_M T_a P_M=T_a,\ \ \ &{\rm for} \ \ \ a=1,...,8,15,\\
P_M T_a P_M=-T_a,\ \ \ &{\rm for} \ \ \ a=9,...,14,
\end{split}$$ so that $U$ can only have the generators $T_a$ with $a=9,...,14$. This way the gauge fields are broken by the boundary condition $P_M$ into $$15\to 8_0+1_0+3_{-4/3}+\bar{3}_{4/3},$$ where the subscript indicate the $U(1)$ charge. The Wilson line restricted by $P_M$ can only give VEVs to the triplets and antitriplets.

After orbifolding we have the effective scalars corresponding to the extra dimensional part of the broken gauge fields behaving like flavons. The gauge fields decompose as $$A_m=\left(\begin{array}{cc} G_\mu-Z'_\mu/3 & \phi\\
\bar{\phi}& Z'_\mu
\end{array}\right),$$ where the flavons in the $3,\overline{3}$ conjugate representations of $SU(3)$ are $$\phi=\frac{1}{2}\left(\begin{array}{c}A_5^{9}+iA_5^{10} \\ A_5^{11}+iA_5^{12} \\A_5^{13}+iA_5^{14}\end{array}\right),\ \ \ \ \bar{\phi}=\frac{1}{2}\left(A_5^{9}-iA_5^{10}, A_5^{11}-iA_5^{12},A_5^{13}-iA_5^{14}\right),$$ which can obtain general VEVs by fixing the Wilson line phase. The flavons, coming from the gauge fields, are 