We present new superalgebra for $\mathcal{N}=2$ $D=3,4$ supergravity theory endowed with the $U(1)$ generator. The superalgebra is rooted in the so-called Soroka-Soroka algebra and spanned by the Lorentz $J_{ab}$ and Lorentz-like $Z_{ab}$, translation $P_a$ and T generators, as well as two supercharges $Q_{\alpha }^I$. It is the only possible realization for a given generator content. We construct a corresponding 3D Chern-Simons supergravity realization of the superalgebra and discuss its relevance.

中文翻译：

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N=2 超重力共振超代数

我们提出了新的超代数$\mathcal{ñ}=2$ $D=3,4$超引力理论赋予$ü(1)$发电机。超代数植根于所谓的 Soroka-Soroka 代数并由 Lorentz${Ĵ}_{\mathrm{一个}b}$和类洛伦兹$Z_{\mathrm{一个}b}$， 翻译${磷}_{\mathrm{一个}}$和T发电机，以及两个增压器${问}_{\alpha }^{我}$. 这是给定生成器内容的唯一可能实现。我们构建了超代数的相应 3D Chern-Simons 超重力实现并讨论了它的相关性。