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The zero mode of an extra-dimensional component of gauge potentials serves as a 4D Higgs field in the gauge-Higgs unification. We examine QED on M⁴ S¹ and determine the mass and potential of a 4D Higgs field (the A₅ component) at the two loop level with gauge invariant reguralization. It is seen that the mass is free from divergences and independent of the renormalization scheme.
Hosotani et al. (Sat,) studied this question.