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We construct the manifestly gauge invariant effective Lagrangian in $3+1$ dimensions describing the standard model in $4+1$ dimensions, following the transverse lattice technique. We incorporate split generation fermions and we explore naturalness for two Higgs configurations: a universal Higgs vacuum expectation value (VEV), common to each transverse brane, and a local Higgs VEV centered on a single brane with discrete exponential attenuation to other branes, emulating the split-generation model. Extra dimensions, with explicit Higgs configurations, do not ameliorate the naturalness problem.
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Cheng et al. (2001) studied this question.
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