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A six-dimensional gauge-Higgs unification model based on $E_6$ gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of $E_6$ on $S^2/Z_2$ orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the $S^2$ and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. Its odd KK-parity makes it a stable particle, and thus a potential dark matter candidate in the model. We also compute the KK masses of all fields at tree level.