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We study the origin of electroweak symmetry under the assumption that$SU(4)_{\rm C} \times SU(2)_{\rm L} \times SU(2)_{\rm R}$ is realized on afive-dimensional space-time. The Pati-Salam type gauge symmetry is reduced to$SU(3)_{\rm C} \times SU(2)_{\rm L} \times U(1)_{\rm R} \times U(1)_{\rm B-L}$by orbifold breaking mechanism on the orbifold $S^1/Z_2$. The breakdown ofresidual gauge symmetries occurs radiatively via the Coleman-Weinbergmechanism, such that the $U(1)_{\rm R} \times U(1)_{\rm B-L}$ symmetry isbroken down to $U(1)_{\rm Y}$ by the vacuum expectation value of an $SU(2)_{\rmL}$ singlet scalar field and the $SU(2)_{\rm L} \times U(1)_{\rm Y}$ symmetryis broken down to the electric one $U(1)_{\rm EM}$ by the vacuum expectationvalue of an $SU(2)_{\rm L}$ doublet scalar field regarded as the Higgs doublet.The negative Higgs squared mass term is originated from an interaction betweenthe Higgs doublet and an $SU(2)_{\rm L}$ singlet scalar field as a Higgsportal. The vacuum stability is recovered due to the contributions fromKaluza-Klein modes of gauge bosons.

Left-right symmetry, orbifold $S^1/Z_2$, and radiative breaking of $U(1)_{\rm R} \times U(1)_{\rm B-L}$