only with the $P$ broken generators $t_{\hat{a}}$ from Eq. \[eq:hatb\] since [^4] $$e^{i\beta^{\hat{a}} Pt_{\hat{a}}P}e^{i\beta^{\hat{a}}t_{\hat{a}}}=e^{-i\beta^{\hat{a}}t_{\hat{a}}}e^{i\beta^{\hat{a}}t_{\hat{a}}}=1.$$ Therefore the effective VEV in the scalar coming from the extra dimension from Eq.\[Wilsonvev\] is $$\braket{A_5^{\hat{b}}}=\frac{\beta^{\hat{b}}}{2\pi R}.$$ This means that only the scalars coming from the fifth component of the gauge field that have a zero mode after orbifolding, can obtain an effective through the Wilson line. In this work we identify these scalars with the flavons $$A_5^{\hat{b}}\sim \phi,$$ whose VEV and its non-Abelian vacuum alignment is fixed through a choice of Wilson lines. To be precise, before orbifolding (and before Wilson lines) the gauge boson $A_5$ is in the adjoint of the higher-dimensional gauge group $G$. After orbifolding, $A_5$ is from the “Coset G/H” where $H$ is the unbroken subgroup of $G$. E.g. If one starts with $SU(5)$ and breaks it to $SU(4) \times U(1)$ by orbifolding, $A_5$ has massless modes only in the $4 + \bar{4}$ of $SU(4)$.

To summarise the mechanism we have been developing, the orbifolding process selects which zero modes survive after compactification by imposing boundary conditions. This effectively breaks the symmetry at low energies and may allow scalars with massless modes. The Wilson Line mechanism generates an effective VEV in 