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Title: Conformal killing spinors in supergravity and related aspects of spin geometry
Author: Rajaniemi, Hannu
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2006
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The aims of this thesis are two-fold: finding a geometric realisation for Nahm’s conformal superalgebras and generalising the concept of a conformal Killing spinor to supergravity, in particular M-theory. We introduce the necessary tools of conformal geometry and construct a conformal Killing superalgebra (that turns out not to be a Lie superalgebra in general) out of the conformal Killing vectors and the conformal Killing spinors of a semi-Riemannian spin manifold and investigate a natural definition of the spinorial Lie derivative that differs from the more commonly used Kosmann-Schwarzbach Lie derivative. We then attempt to generalise the definition of conformal Killing spinors to M-theory and characterise M-theory backgrounds admitting such spinors. We also construct a M-theory analogue of the conformal Killing superalgebra. We show that further examples can be constructed in type IIA and in the massive IIA theory of Howe, Lambert and West via Kaluza-Klein reduction. We also comment on a curious identity involving the Penrose operator in type IIB supergravity. Finally – building on known results about the relationship between the dimension of the space of conformal Killing spinors on a non-simply connected manifold and the choice of spin structure – we explore the importance of the choice of spin structure in determining the amount of supersymmetry preserved by a symmetric M-theory background constructed by quotienting a supersymmetric Hpp-wave with a discrete subgroup in the centraliser of its isometry group.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available