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Low scale quantum gravity in gauge-Higgs unified models

We consider the scale at which gravity becomes strong in linearized General Relativity coupled to the gauge-Higgs unified(GHU) model. We also discuss the unitarity of S-matrix in the same framework. The Kaluza-Klein(KK) gauge bosons, KK scalars and KK fermions in the GHU models can drastically change the strong gravity scale and the unitarity violation scale. In particular we consider two models GHU_SM and GHU_MSSM which have the zero modes corresponding to the particle content of the Standard Model and the Minimal Supersymmetric Standard Model, respectively. We find that the strong gravity scale could be lowered as much as 10^13 (10^14) GeV in the GHU_SM (GHU_MSSM) for one extra dimension taking 1 TeV as the compactification scale. It is also shown that these scales are proportional to the inverse of the number of extra dimensions d. In the d=10 case, they could be lowered up to 10^5 GeV for both models. We also find that the maximum compactification scales of extra dimensions quickly converge into one special scale M_O near Planck scale or equivalently into one common radius R_0 irrespectively of d as the number of zero modes increases. It may mean that all extra dimensions emerge with the same radius near Planck scale. In addition, it is shown that the supersymmetry can help to remove the discordance between the strong gravity scale and the unitarity violation scale.