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The derived pure spinor formalism as an equivalence of categories

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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 super-translation algebra and equivariant modules over its Chevalley-Eilenberg cochains. This equivalence is closely linked to Koszul dual...

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Main Authors: Elliott, Chris (Author) , Hahner, Fabian (Author) , Saberi, Ingmar (Author)
Format: Article (Journal) Chapter/Article
Language:English
Published: 27 May 2022
Edition:Version v2
In: Arxiv
Year: 2022, Pages: 1-49
DOI:10.48550/arXiv.2205.14133
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2205.14133
Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2205.14133
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Author Notes:Chris Elliott, Department of Mathematics and Statistics, University of Massachusetts at Amherst, 710 N. Pleasant St. Amherst, MA 01003, U.S.A., Fabian Hahner, Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Deutschland, Ingmar Saberi, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 München, Deutschland
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Summary: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 super-translation 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.
Item Description:Version 1 vom 11 Juli 2022, Version 2 vom 27 Mai 2022
Gesehen am 18.10.2022
Physical Description:Online Resource
DOI:10.48550/arXiv.2205.14133

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