The field transformation that removes the Higgs locally except at the IR brane is identical to a gauge transformation with gauge parameter This is not an actual gauge transformation because this gauge parameter does not satisfy the corresponding boundary conditions, but it eliminates the Higgs boson locally except at the IR brane. The bulk action for the rotated fields is then free of the Higgs v.e.v. v$_{H}$ , and it can be solved analytically as we did before. The boundary conditions at the UV brane remain the same, since ρ ( R ) = 1. However, the boundary conditions at the IR brane in Eq. (18) apply to the original fields and when written in terms of the rotated ones, they will explicitly include the Higgs effects. Note that the physical modes will now participate from all multiplets, not only from those mixed by localized terms but from those mixed by the Higgs, too. This makes the corresponding boundary conditions much more challenging. Also note that, since we are imposing now as boundary conditions the UV localized Majorana masses, we necessarily have to deal with all three generations simultaneously in the neutrino expansion. For instance, once we impose the UV boundary conditions, the Higgs dependent IR boundary conditions give a system of 8 equations with 8 unknowns (per family) for the charge − 1 leptons and two independent systems of 24 equations with 24 unknowns for the neutral ones (due to the Majorana boundary condition the three families mix and the corresponding system of 24 equations with 24 complex unknowns splits into real and imaginary parts, as discussed in Appendix B). Requiring a non-trivial solution of the corresponding systems fixes the mass of the physical states and determines all unknowns in terms of one normalization constant, which is then fixed by the normalization condition involving all relevant multiplets. The exact expression for these boundary conditions are too large to be included here but we have checked that the masses of the charged and neutral leptons (for simplicity we have neglected inter-generational mixing) are in excellent agreement with those obtained with a perturbative treatment of Higgs and UV Majorana mass effects. ζ ′ = ρζ (53) ρ ( z, v$_{H}$ ) = exp [ i √$_{2}$$_{g}$$_{5}$$_{v}$$_{H}$$_{T}$ 4 C √ R ( R ′ 2 − R $^{2}$) ∫ z R dz ′ z ′ ] ≈ exp [ igv$_{H}$T 4 C √ log( R ′ /R ) / 2 ( z 2 − R 2 R ′ )] . (52) 17