To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification

Abstract

In this paper, we investigate the finiteness of the Higgs effective potential in an SU(N) Gauge-Higgs Unification (GHU) model defined on M4× S1. 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) gauge theory on M5× S1, 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.