Adinkras and pure spinors

• Verfasst von: Eager, Richard [VerfasserIn]
• Verfasst von: Noja, Simone [VerfasserIn]
• Verfasst von: Senghaas, Raphael [VerfasserIn]
• Verfasst von: Walcher, Johannes [VerfasserIn]
• Titel: Adinkras and pure spinors
• Verf.angabe: Richard Eager, Simone Noja, Raphael Senghaas, Johannes Walcher
• Ausgabe: Version v2
• E-Jahr: 2024
• Jahr: 4 Sep 2024
• Umfang: 91 S.
• Illustrationen: Illustrationen
• Fussnoten: Gesehen am 16.09.2024
• Titel Quelle: Enthalten in: Arxiv
• Ort Quelle: Ithaca, NY : Cornell University, 1991
• Jahr Quelle: 2024
• Band/Heft Quelle: (2024) vom: Sept., Artikel-ID 2404.07167, Seite 1-91
• DOI: doi:10.48550/arXiv.2404.07167
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematical Physics
• K10plus-PPN: 1902579143

Abstract

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.