作为范畴等价的派生纯Spinor形式主义

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-05-27 DOI:10.3842/SIGMA.2023.022
C. Elliott, F. Hahner, Ingmar Saberi
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引用次数: 3

摘要

我们构造了纯旋量超场形式的派生推广,并证明了它在超平移代数的多重态和Chevalley-Eilenberg共域上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。在介绍和描述了超多重态的范畴之后,我们将导出的纯旋量构造明确地定义为dg函子。然后,我们使用显式计算证明了取任何超多重集的导出超平移不变量的函子是纯旋量结构的拟逆。最后,我们用例子说明了我们的发现,并利用衍生形式主义的见解来回答一些关于普通(假设不足)纯旋量超场形式主义的问题。
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The Derived Pure Spinor Formalism as an Equivalence of Categories
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.
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
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