Stability of the Higgs mass in theories with extra dimensions † Abstract We analyze the ultraviolet stability of the Higgs mass in recently proposed Kaluza-Klein models com-pactified on S 1 /Z 2 or S 1 /(Z 2 × Z ′ 2), both at the field theory and string theory level. Fayet-Iliopoulos terms of U (1) hypercharge are shown to be of vital importance for this discussion. Models with a single Higgs d...