| Summary: | Abstract In this paper, we investigate the finiteness of the Higgs effective potential in an SU( N $$ \mathcal{N} $$ ) Gauge-Higgs Unification (GHU) model defined on M4 × S 1. We obtain the Higgs effective potential at the two-loop level and find that it is finite. We also discuss that the Higgs effective potential is generically divergent for three- or higher-loop levels. As an example, we consider an SU( N $$ \mathcal{N} $$ ) gauge theory on M5 × S 1, where the one-loop corrections to the four-Fermi operators are divergent. We find that the Higgs effective potential depends on their counter terms at the three-loop level.
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