2024/04/10 by Eager, Richard, Noja, Simone, Senghaas, Raphael +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2404.07167
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.