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 o
ut 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.
We show the bounds on five- and six-dimensional Universal Extra Dimension models from the result of the Higgs boson searches at the Large Hadron Collider and electroweak precision measurement. The latest data released by the ATLAS and the CMS gives t
he lower bounds on Kaluza-Klein scale which are from 650 GeV to 1350 GeV depending on models from Higgs to diboson/diphoton decay signal. The Higgs production cross section can be enhanced by factor 1.5 in crude estimation, diphoton decay signal is suppressed about 10%. Electroweak precision measurement also gives the lower bounds as from 700 GeV to 1500 GeV.
