Extended supersymmetry in Dirac action with extra dimensions

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Abstract

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.

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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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