Nilpotence varieties

• Verfasst von: Eager, Richard [VerfasserIn]
• Verfasst von: Saberi, Ingmar [VerfasserIn]
• Verfasst von: Walcher, Johannes [VerfasserIn]
• Titel: Nilpotence varieties
• Verf.angabe: Richard Eager, Ingmar Saberi and Johannes Walcher
• E-Jahr: 2021
• Jahr: January 16, 2021
• Umfang: 58 S.
• Fussnoten: Gesehen am 18.06.2021
• Titel Quelle: Enthalten in: Institut Henri PoincaréAnnales Henri Poincaré
• Ort Quelle: Cham (ZG) : Springer International Publishing AG, 2000
• Jahr Quelle: 2021
• Band/Heft Quelle: 22(2021), 4, Seite 1319-1376
• ISSN Quelle: 1424-0661
• DOI: doi:10.1007/s00023-020-01007-y
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1760868140
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

We consider algebraic varieties canonically associated with any Lie superalgebra, and study them in detail for super-Poincaré algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of) the odd part of the algebra. Most of these varieties have appeared in various guises in previous literature, but we study them systematically here, from a new perspective: As the natural moduli spaces parameterizing twists of a super-Poincaré-invariant physical theory. We obtain a classification of all possible twists, as well as a systematic analysis of unbroken symmetry in twisted theories. The natural stratification of the varieties, the identification of strata with twists, and the action of Lorentz and R-symmetry are emphasized. We also include a short and unconventional exposition of the pure spinor superfield formalism, from the perspective of twisting, and demonstrate that it can be applied to construct familiar multiplets in four-dimensional minimally supersymmetric theories.