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Six Dimensional Gauge-Higgs Unification with an Extra Space S^2 and the Hierarchy Problem
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We calculate one-loop radiative correction to the mass of Higgs identified with the extra space components of the gauge field in a six dimensional massive scalar QED compactified on a two-sphere. The radiatively induced Higgs mass is explicitly shown to be finite for arbitrary bulk scalar mass M. Furthermore, the remaining finite part also turns out to vanish, at least for the case of small M, thus suggesting that the radiatively induced Higgs mass exactly vanishes, in general. The non-zero "Kaluza-Klein" modes in the gauge sector are argued to have a Higgs-like mechanism and quantum mechanical N=2 supersymmetry, while the Higgs zero modes, as supersymmetric states, have a close relation with monopole configuration.
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Gauge symmetry breaking with $S^2$ extra dimensions
On S2, a cos θ background gauge field breaks the gauge group to its centralizer; the KK mass spectrum is (j(j+1) - kα^2)/R^2 for charged modes.
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