We apply the Lie algebra expansion method to the $\mathcal{N}=1$ super-Poincare algerba in four dimensions. We define a set of p-brane projectors that induce a decomposition of the super-Poincare algebra preparatory for the expansion. We show that starting from the $\mathcal{N}=1$ supergravity action in four dimensions it is possible to obtain two non-relativistic supersymmetric theories, one describing strings, the other membranes.

中文翻译：

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非相对论四维 p-膜超对称理论和李代数展开

我们在四个维度上将李代数展开方法应用于 $\mathcal{N}=1$ 超级庞加莱代数。我们定义了一组 p-brane 投影仪，它们诱导超庞加莱代数的分解，为展开做准备。我们表明，从 $\mathcal{N}=1$ 的四维超引力作用开始，可以获得两种非相对论超对称理论，一种描述弦，另一种描述膜。