标题： 导出纯旋量形式主义作为范畴的等价性 显示英文标题

标题： The Derived Pure Spinor Formalism as an Equivalence of Categories

摘要： 我们构建了纯旋量超场形式的导出推广，并证明它在超平移代数的多重态与它的Chevalley-Eilenberg上循环的等变模之间表现出dg-范畴的等价性。 这种等价性与超平移代数的Koszul对偶密切相关。 在介绍了并描述了超多重态的范畴之后，我们明确地将导出纯旋量构造定义为一个dg-函子。 然后，我们通过显式计算表明，取任何超多重态的导出超平移不变量的函子是纯旋量构造的拟逆。 最后，我们通过例子说明我们的发现，并利用导出形式主义的见解来回答一些关于普通（非导出）纯旋量超场形式的问题。 显示英文摘要

摘要： 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.