Fermions in Kaluza-Klein and Randall-Sundrum Theories

TL;DR

This paper compares fermion behavior in Kaluza-Klein and Randall-Sundrum theories, revealing dual properties, localization, and CP-violation origins through detailed analysis of fermion interactions and quantum effects.

Contribution

It provides a comparative analysis of fermions in KK and RS models, highlighting dual properties, localization, and the emergence of CP-violation from quantum effects.

Findings

Dual electric and magnetic dipole moments in KK model.

Electric dipole moment term appears naturally in RS model.

Dual relation between KK and RS models in the 4D limit.

Abstract

The Kaluza-Klein theory and Randall-Sundrum theory are examined comparatively, with 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, 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 the CP-violation. In the 4D limit, the dual relation between KK model and RS model appears.