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 $\mathrm{SU}(\mathcal{N})$ Gauge-Higgs Unification (GHU) model defined on ${\mathbf{M}}^4\times S^1$. 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 $\mathrm{SU}(\mathcal{N})$ gauge theory on ${\mathbf{M}}^5\times S^1$, 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.

Comments: 23 pages. Accepted for publication in JHEP