Construction of the Higgs potential with spontaneous CP violation in terms of the gauge theory on the z2 × z3 group

The gauge theory on the z2 × z3 group is presented according to the general formalism of the gauge theory on the discrete group. The Yang-Mills action, i.e., the Higgs potential is constructed with the assumption of the gauge fields consisting of three Higgs doublets and the assumption of the metric on the differential algebra. There are two types of solutions to the constrained equations imposed on the vacuum expected values of the three Higgs doublets, one conserving the CP symmetry and the other violating it. The violating solution corresponds to the true vacuum.