论文标题
派生的纯纺纱形式主义是类别的等效性
The Derived Pure Spinor Formalism as an Equivalence of Categories
论文作者
论文摘要
我们构建了纯旋转超级场外形式主义的衍生概括，并证明它在其Chevalley-eilenberg Cochains上表现出对超倾斜代数的多重组和均衡模块的等效性。这种等效性与超级译本代数的Koszul二元性密切相关。在介绍和描述了超级植物的类别之后，我们将衍生的纯纺纱构造明确定义为DG函数。然后，我们证明使用明确的计算，采用任何超级摩尔植物的派生超跨化不变性是对纯旋转构建的准内词。最后，我们用示例说明了我们的发现，并利用派生形式主义的见解来回答有关普通（未经）纯净旋转器超级场外形式主义的一些问题。
We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra and equivariant modules over its Chevalley-Eilenberg cochains. This equivalence is closely linked to Koszul duality for the supertranslation algebra. After introducing and describing the category of supermultiplets, we define the derived pure spinor construction explicitly as a dg-functor. We then show that the functor that takes the derived supertranslation invariants of any supermultiplet is a quasi-inverse to the pure spinor construction, using an explicit calculation. Finally, we illustrate our findings with examples and use insights from the derived formalism to answer some questions regarding the ordinary (underived) pure spinor superfield formalism.
