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We construct the zero temperature (no compact dimensions) effective actionfor an SU(2) Yang-Mills theory in five dimensions, with boundary conditionsthat reduce the symmetry on the four-dimensional boundary located at the originto a U(1)-complex scalar system. In order to be sensitive to the Higgs phase,we need to include higher dimensional operators in the effective action, whichcan be naturally achieved by generating it by expanding the correspondinglattice construction in small lattice spacing, taking the naive continuum limitand then renormalizing. In addition, we build in the effective actionnon-perturbative information, related to a first order quantum phase transitionknown to exist. As a result, the effective action acquires a finite cut-offthat is low and the fine tuning of the scalar mass is rather mild.

RG flows in Non-Perturbative Gauge-Higgs Unification II. Effective action for the Higgs phase near the quantum phase transition