Adinkras and pure spinors
The nilpotence variety for extended supersymmetric quantum mechanics is a cone over a quadric in projective space. The pure spinor correspondence, which relates the description of off-shell supermultiplets to the classification of modules over the corresponding hypersurface ring, reduces to a classi...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
4 Sep 2024
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| Edition: | Version v2 |
| In: |
Arxiv
Year: 2024, Pages: 1-91 |
| DOI: | 10.48550/arXiv.2404.07167 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.48550/arXiv.2404.07167 Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2404.07167 
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| Author Notes: | Richard Eager, Simone Noja, Raphael Senghaas, Johannes Walcher |
| Summary: | The nilpotence variety for extended supersymmetric quantum mechanics is a cone over a quadric in projective space. The pure spinor correspondence, which relates the description of off-shell supermultiplets to the classification of modules over the corresponding hypersurface ring, reduces to a classical problem of linear algebra. Spinor bundles, which correspond to maximal Cohen-Macaulay modules, serve as basic building blocks. Koszul duality appears as a deformed version of the Bernstein-Gel'fand-Gel'fand correspondence that we make fully concrete. We illustrate in numerous examples the close relationship between these connections and the powerful graphical technology of Adinkras, which appear as a decategorification of special complexes on quadrics. We emphasize the role of R-symmetry for recovering higher-dimensional gauge and gravity multiplets. |
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| Item Description: | Gesehen am 16.09.2024 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2404.07167 |