Fermions in Kaluza-Klein and Randall-Sundrum theories

The Kaluza-Klein (KK) and Randall-Sundrum (RS) theories are examined comparatively, with a focus on the behavior of the five-dimensional (Dirac) fermion in the dimensional reduction to four dimensions. They are properly treated using the Cartan formalism. In the KK case, the dual property between the electric and magnetic dipole moments is revealed in relation to the ratio of two massive parameters: the inverse of the radius of the extra-space circle and the 5D fermion mass. The order estimation of the couplings is done. In the RS case, we consider the interaction with the 5D (bulk) Higgs field and the gauge field. The chiral property, localization, and anomaly phenomena are examined. We evaluate the bulk quantum effect using the method of the induced effective action. The electric dipole moment term naturally appears. This is a new origin of $\mathrm{CP}$ violation. In the 4D limit, the dual relation between the KK model and the RS model appears.