content_image/365593.jpg content_image/365594.jpg
source of violation of TBM and the non-diagonal X$_{l}$ a source of FCNC for the charged leptons. This implies some constraint on v $^{(}$′) ( η $_{)}$/ Λ $^{(}$′) that will be discussed in the next section. 

We have neglected so far in our discussion the effect of brane kinetic terms (BKT). 

These are generated by quantum corrections and therefore cannot be set to zero at arbitrary scales [40]. The global symmetries of our model, however, strongly constrain them. In particular, all possible BKT are proportional to the identity at leading order in A$_{4}$ and Z$_{8}$ breaking, except those involving ζ$_{α}$ fields, which are diagonal but flavor dependent. 

Corrections to this pattern are of order v $^{2}$/ Λ $^{2}$, where v and Λ stand here for any v, v$_{η}$, v ′ , v ′ η and Λ , Λ ′ , respectively. Since at leading order there is no flavor violation in the charged lepton sector, these flavor dependent (but diagonal) BKT do not generate FCNC. Once higher order terms are included, there is a small flavor violation in the charged lepton sector and therefore the flavor dependent BKT will induce FCNC. Higher order contributions to BKT breaking A$_{4}$ are also a potential source of flavor violation. However, the A$_{4}$ and Z$_{8}$ symmetries ensure that the v ′ $^{2}$/ Λ ′ 2 corrections are diagonal. Therefore, their effect is subleading and we will disregard them here. Hence, we include higher order effects in the localized mass terms but not in the BKT. The effects of diagonal BKT are well-known (see for instance [41]). They do not change the functional dependence of the fermion zero modes and only affect their normalization. The ones leading to flavor violation are the BKTs for the RH component of the SO (4) singlet in ζ$_{α}$ (all the other ones are proportional to the identity, up to tiny corrections). The corresponding BKT can be written as 

<img src='content_image/365593.jpg'>

where κ α is a dimensionless coefficients parametrizing the BKTs. The fermion zero modes for the RH charge − 1 leptons have the same functional form as in the absence of BKT, Eqs. (27) and (28), except for the normalization that is now 

<img src='content_image/365594.jpg'>

Note that f 2 − c ≪ 1 for c ≲ − 0 . 4 so this effect in the normalization can be only relevant for the tau lepton. A more significant effect regarding flavor is that the covariant derivative 

