Abstract
A new realization of extended quantum-mechanical supersymmetry (QM SUSY) with central extension is investigated. We first show that two different sets of $d+2$ ($d+1$) supercharges for $d=$ even (odd), each of which satisfies an $\mathcal{N}=d+2$ ($d+1$) extended QM SUSY algebra without central extension, are hidden in the four-dimensional (4D) mass spectrum of the $(4+d)$-dimensional Dirac action. We then find that the whole set of the supercharges forms an $\mathcal{N}=2d+4$ ($2d+2$) extended QM SUSY algebra with central charges for $d=$ even (odd). The representation of the supersymmetry algebra is shown to be $1/2$-Bogomol'nyi--Prasad--Sommerfield states that correspond to a short representation for the supersymmetry algebra with central extension. We explicitly examine the 4D mass spectrum of the models with the hyperrectangle and the torus extra dimensions, and discuss their supersymmetric structures.
Highlights
Quantum-mechanical supersymmetry (QM SUSY) is well known as the supersymmetry realized in quantum mechanics, which was introduced by Witten [1] to investigate the supersymmetry breaking
In Refs. [24,25], we have revealed that the N 1⁄4 2 quantum-mechanical supersymmetry (QM SUSY) structure exists in the four-dimensional (4D) mass spectrum of the six-dimensional Dirac action
We have revealed that the N -extended QM SUSY with the central charges is hidden in the 4D mass spectrum of the higher dimensional Dirac action
Summary
Quantum-mechanical supersymmetry (QM SUSY) is well known as the supersymmetry realized in quantum mechanics, which was introduced by Witten [1] to investigate the supersymmetry breaking. We discuss a new realization of N -extended QM SUSY with central extension We find another set of 2bd=2c þ 2 supercharges in the (4 þ d)-dimensional Dirac action, which forms the same N 1⁄4 2bd=2c þ 2 QM SUSY algebra as that given in Ref. We show that the whole set of the 4bd=2c þ 4 supercharges forms an N 1⁄4 4bd=2c þ 4 extended QM SUSY algebra with central charges, and that the representation of the supersymmetry algebra forms a short multiplet corresponding to 1=2-BPS states. This paper is organized as follows: In Sec. II, we summarize the KK decomposition of a (4 þ d)-dimensional Dirac field and show that the N 1⁄4 2 QM SUSY is hidden in the 4D mass spectrum. Dimensional Dirac action and the doubly degenerate states ðf ðαnÞðyÞ; 0ÞT and ð0; gðαnÞðyÞÞT are mutually related by the supercharge Q, except for zero energy states
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