We consider a six-dimensional theory with a scalar field whose Higgs-type potential is localized at the origin of the compact transverse dimensions. Resolving the brane singularity yields renormalization group evolution for the localized couplings at the classical level. For instance, a tachyonic mass term grows in the IR and hits a Landau pole. There appears a particular value of the coupling such that the running mass parameter becomes large precisely at the compactification scale. For values of the coupling above this critical point, spontaneous symmetry breaking takes place and the zero mode is very light.
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