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 duali...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2023 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211921 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Derived Pure Spinor Formalism as an Equivalence of Categories. Chris Elliott, Fabian Hahner and Ingmar Saberi. SIGMA 19 (2023), 022, 37 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727743421022208 |
|---|---|
| author | Elliott, Chris Hahner, Fabian Saberi, Ingmar |
| author_facet | Elliott, Chris Hahner, Fabian Saberi, Ingmar |
| citation_txt | The Derived Pure Spinor Formalism as an Equivalence of Categories. Chris Elliott, Fabian Hahner and Ingmar Saberi. SIGMA 19 (2023), 022, 37 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-21T11:08:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211921 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:08:30Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Elliott, Chris Hahner, Fabian Saberi, Ingmar 2026-01-16T11:20:04Z 2023 The Derived Pure Spinor Formalism as an Equivalence of Categories. Chris Elliott, Fabian Hahner and Ingmar Saberi. SIGMA 19 (2023), 022, 37 pages 1815-0659 2020 Mathematics Subject Classification: 81R25; 17B55; 17B81 arXiv:2205.14133 https://nasplib.isofts.kiev.ua/handle/123456789/211921 https://doi.org/10.3842/SIGMA.2023.022 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. We would like to give special thanks to R. Eager, J. Walcher, and B. R. Williams for conversations and collaboration on related projects. We also gratefully acknowledge conversations with I. Brunner, M. Cederwall, I. Contreras, O. Gwilliam, J. Huerta, J. Palmkvist, and S. Noja. In addition, we would like to thank the anonymous referees for their useful suggestions. This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1– 390900948 (the Heidelberg STRUCTURES Excellence Cluster). I.S. is supported by the Free State of Bavaria. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Derived Pure Spinor Formalism as an Equivalence of Categories Article published earlier |
| spellingShingle | The Derived Pure Spinor Formalism as an Equivalence of Categories Elliott, Chris Hahner, Fabian Saberi, Ingmar |
| title | The Derived Pure Spinor Formalism as an Equivalence of Categories |
| title_full | The Derived Pure Spinor Formalism as an Equivalence of Categories |
| title_fullStr | The Derived Pure Spinor Formalism as an Equivalence of Categories |
| title_full_unstemmed | The Derived Pure Spinor Formalism as an Equivalence of Categories |
| title_short | The Derived Pure Spinor Formalism as an Equivalence of Categories |
| title_sort | derived pure spinor formalism as an equivalence of categories |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211921 |
| work_keys_str_mv | AT elliottchris thederivedpurespinorformalismasanequivalenceofcategories AT hahnerfabian thederivedpurespinorformalismasanequivalenceofcategories AT saberiingmar thederivedpurespinorformalismasanequivalenceofcategories AT elliottchris derivedpurespinorformalismasanequivalenceofcategories AT hahnerfabian derivedpurespinorformalismasanequivalenceofcategories AT saberiingmar derivedpurespinorformalismasanequivalenceofcategories |