content_image/367288.jpg content_image/367285.jpg content_image/367286.jpg content_image/367287.jpg
the boundary conditions, and local and global symmetries, can be written 

<img src='content_image/367288.jpg'>

where we have assumed that lepton number is only violated on the UV brane. 3 l denotes the SM-like doublet and ˜ l stands for the other SU (2)$_{L}$ doublet within the given bi-doublet, whereas the dots correspond to higher dimensional operators. We have also introduced the LH and RH chirality projections ζ$_{L,R}$ ≡ [(1 ∓ γ $^{5}$) / 2] ζ , recovering the standard 4D notation. Finally, ( ) α , α = e, µ, τ , are the 3 × 3 combinations transforming under A$_{4}$ as 1 , 1 ′′ and 1 ′ , respectively. 

As usually in these models, we shall assume that A$_{4}$ × Z$_{8}$ is spontaneously broken by the boundary scalar vacuum expectation values (v.e.v.) 

<img src='content_image/367285.jpg'>

resulting in the brane localized terms 

<img src='content_image/367286.jpg'>

with the Majorana mass matrix 

<img src='content_image/367287.jpg'>

