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 KaluzaKlein decomposition for the higher dimensional Dirac field, that is, KaluzaKlein mode functions of 4D right-handed spinors and 4D left-handed ones form N = 2 supermultiplets. 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.
CITATION STYLE
Fujimoto, Y., Hasegawa, K., Nishiwaki, K., Sakamoto, M., Tatsumi, K., & Ueba, I. (2018). Extended supersymmetry in Dirac action with extra dimensions. Journal of Physics A: Mathematical and Theoretical, 51(43). https://doi.org/10.1088/1751-8121/aadea2
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