Perspectives on the pure spinor superfield formalism

• Verfasst von: Eager, Richard [VerfasserIn]
• Verfasst von: Hahner, Fabian [VerfasserIn]
• Verfasst von: Saberi, Ingmar [VerfasserIn]
• Verfasst von: Williams, Brian R. [VerfasserIn]
• Titel: Perspectives on the pure spinor superfield formalism
• Verf.angabe: Richard Eager, Fabian Hahner, Ingmar Saberi, Brian R. Williams
• E-Jahr: 2022
• Jahr: October 2022
• Umfang: 47 S.
• Fussnoten: Online verfügbar am 18. Juli 2022, Artikel-Version vom 27 Juli 2022 ; Gesehen am 10.10.2022
• Titel Quelle: Enthalten in: Journal of geometry and physics
• Ort Quelle: Amsterdam [u.a.] : North-Holland, 1984
• Jahr Quelle: 2022
• Band/Heft Quelle: 180(2022), Artikel-ID 104626, Seite 1-47
• DOI: doi:10.1016/j.geomphys.2022.104626
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: BV formalism
• Sach-SW: Homotopy transfer
• Sach-SW: Pure spinors
• Sach-SW: Representation theory of super-Poincaré algebras
• Sach-SW: Superspace methods
• K10plus-PPN: 1818347210

Abstract

In this note, we study, formalize, and generalize the pure spinor superfield formalism from a rather nontraditional perspective. To set the stage, we review the notion of a multiplet for a general super Lie algebra, working in the context of the BV and BRST formalisms. Building on this, we explain how the pure spinor superfield formalism can be viewed as constructing a supermultiplet out of the input datum of an equivariant graded module over the ring of functions on the nilpotence variety. We use the homotopy transfer theorem and other computational techniques from homological algebra to relate these multiplets to more standard component-field formulations. Physical properties of the resulting multiplets can then be understood in terms of algebrogeometric properties of the nilpotence variety. We illustrate our discussion with many examples in various dimensions.