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.
Notes on sphere-based universal extra dimensions
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We review the six dimensional universal extra dimension models compactified on the sphere $S^2$, the orbifold $S^2/Z_2$, and the projective sphere, which are based on the spontaneous compactification mechanism on the sphere. In particular, we spell out the application of the Newman-Penrose eth-formalism on these models with some technical details on the derivation of the Kaluza-Klein modes and their interactions, and revisit the problem in the existence of the zero mode of $U(1)_X$ additional gauge boson required for the spontaneous compactification. We also explain the theoretical background on the vacuum stability argument for the upper bound on the ultraviolet cutoff scale.
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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.