We revisit the novel symmetries in $\mathcal{N}$ = 2 supersymmetric (SUSY) quantum mechanical (QM) models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator. Moreover, we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.

中文翻译：

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重新审视耦合 ${ \mathcal N }=2$ 超对称量子系统中的新对称性：示例和超变量方法

我们通过考虑耦合系统的具体例子，重新审视 $\mathcal{N}$ = 2 超对称 (SUSY) 量子力学 (QM) 模型中的新对称性。此外，我们将分析扩展到一般情况并列出所有新的对称性。在每种情况下，我们都展示了两组离散对称性的存在，它们对应于微分几何的霍奇对偶算子。因此，我们能够提供猜想的证明，该猜想指出存在多个对应于霍奇对偶算子的离散对称变换。此外，我们在超变量方法的框架内推导出广义超势的壳上幂零对称性。