title: The Pure Spinor Superfield Formalism and Twisted Supergravity
creator: Hahner, Fabian
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
subject: ddc-530
subject: 530 Physics
description: This thesis discusses the pure spinor superfield formalism and its applications, specifically in the context of twisted eleven-dimensional supergravity. We start by developing the pure spinor superfield formalism as a framework for the construction of supermultiplets from a graded equivariant module over the ring of functions on the nilpotence variety. This perspective establishes a connection between algebrogeometric properties of the nilpotence variety and the physics of multiplets. Furthermore, it allows for efficient computations by means of homological algebra. After exploring the formalism in various examples, we extend it to the setting of derived geometry, show that this generalization establishes an equivalence of categories, and relate it to Koszul duality. In particular, this result establishes a method to construct superspace descriptions for any multiplet. As an application, we provide an extensive case study of supermultiplets with six-dimensional $\cN=(1,0)$ supersymmetry and classify all multiplets whose derived invariants for the supertranslation algebra define a line bundle on the nilpotence variety. In the second part, we consider eleven-dimensional supergravity and its twists. We compute the maximal twist in the free perturbative limit starting from the $L_\infty$ action of the super Poincar\'e algebra on the BV complex of component fields. Then, we use the pure spinor superfield formalism to construct a generalization of Poisson--Chern--Simons theory, defined on any supermanifold equipped with an appropriate odd distribution. This theory recovers Cederwall's formulation of eleven-dimensional supergravity, Costello's description of the maximal twist, and gives a pure spinor lift of the interactions in the minimally twisted theory. Compatibility between the pure spinor formalism and twisting implies that all these theories are related by twists. Motivated by holographic duality, we use these methods to explore (twisted) six-dimensional (2,0) supersymmetry. We give a pure spinor construction of the decomposition of the minimally twisted eleven-dimensional supergravity fields into $E(3|6)$-modules and provide an interpretation in terms of supergeometry which hints towards a generalization in the untwisted case.
date: 2024
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/34380/1/Thesis-Fabian-Hahner.pdf
identifier: DOI:10.11588/heidok.00034380
identifier: urn:nbn:de:bsz:16-heidok-343808
identifier:   Hahner, Fabian  (2024) The Pure Spinor Superfield Formalism and Twisted Supergravity.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/34380/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng