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arXiv · 1804.02626

Extended supersymmetry in Dirac action with extra dimensions

Yukihiro Fujimoto·Kouhei Hasegawa·Kenji Nishiwaki·Makoto Sakamoto·Kentaro Tatsumi·Inori Ueba
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Abstract

We investigate a new realization of extended quantum-mechanical supersymmetry. We first show that an $\mathcal{N}=2$ 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 $\mathcal{N}=2$ supermultiplets. In addition to $\mathcal{N}=2$ supersymmetry, we discover that an $\mathcal{N}$-extended supersymmetry ($\mathcal{N} = d+2\ (d+1)$ 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 $\mathcal{N}$-extended supercharges and clarify the condition to preserve the supersymmetry. The partial breaking of the supersymmetry is also demonstrated.

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Yukihiro Fujimoto, Kouhei Hasegawa, Kenji Nishiwaki, Makoto Sakamoto, Kentaro Tatsumi, Inori Ueba. 2018-04-08. Extended supersymmetry in Dirac action with extra dimensions. https://arxiv.org/abs/1804.02626

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