Extended supersymmetry in Dirac action with extra dimensions

We investigate a new realization of extended quantum-mechanical supersymmetry. We first show that an N = 2 quantum-mechanical supersymmetry is hidden in the four-dimensional (4D) spectrum of the Kaluza-Klein decomposition for the higher dimensional Dirac field, that is, Kaluza-Klein mode functions of 4D right-handed spinors and 4D left-handed ones form N = 2 supennultiplets. In addition to N = 2 supersymmetry, we discover that an N-extended supersymmetry (N = d + 2 (d + 1) for d = even (odd) extra dimensions) is further hidden in the 4D spectrum. The extended symmetry can explain additional degeneracy of the spectrum. Furthermore, we show that a superpotential can be introduced into the N-extended supercharges and clarify the condition to preserve the supersymmetry. The partial breaking of the supersymmetry is also demonstrated.