We consider algebraic varieties canonically associated with any Lie superalgebra, and study them in detail for super-Poincaré algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of) the odd part of the algebra. Most of these varieties have appeared in various guises in previous literature, but we study them systematically here, from a new perspective: As the natural moduli spaces parameterizing twists of a super-Poincaré-invariant physical theory. We obtain a classification of all possible twists, as well as a systematic analysis of unbroken symmetry in twisted theories. The natural stratification of the varieties, the identification of strata with twists, and the action of Lorentz and R-symmetry are emphasized. We also include a short and unconventional exposition of the pure spinor superfield formalism, from the perspective of twisting, and demonstrate that it can be applied to construct familiar multiplets in four-dimensional minimally supersymmetric theories. In all dimensions and with any amount of supersymmetry, this technique produces BRST or BV complexes of supersymmetric theories from the Koszul complex of the maximal ideal over the coordinate ring of the nilpotence variety, possibly tensored with any equivariant module over that coordinate ring. In addition, we remark on a natural connection to the Chevalley–Eilenberg complex of the supertranslation algebra, and give two applications related to these ideas: a calculation of Chevalley–Eilenberg cohomology for the (2, 0) algebra in six dimensions, and a degenerate BV complex encoding the type IIB supergravity multiplet.

我们考虑与任何李超代数典范相关的代数变体，并针对物理兴趣的超级庞加莱代数进行详细研究。它们是代数奇数部分中（投影的奇偶性逆转）的幂等元素的源头。这些变体中的大多数已出现在以前的文献中的各种形式中，但是我们在这里从一个新的角度系统地研究它们：作为自然模空间，参数化了超庞加莱不变物理理论的扭曲。我们获得了所有可能扭曲的分类，以及对扭曲理论中不间断对称性的系统分析。品种的自然分层，扭曲地层的识别以及洛伦兹和R的作用强调对称性。我们还从扭曲的角度对纯旋子超场形式主义进行了简短而非常规的阐述，并证明了它可用于在四维极小超对称理论中构建熟悉的多重峰。在所有维度上，并以任何数量的超对称性，该技术均根据幂等变体的坐标环上最大理想的Koszul复数生成超对称理论的BRST或BV复数，并可能对该坐标环上的任何等变模量进行张量。此外，我们评论了与超翻译代数的Chevalley-Eilenberg复数的自然联系，并给出了与这些思想相关的两个应用：（6，0）代数（2，0）的Chevalley-Eilenberg同调，