Killing Spinors -- Beyond Supergravity

Abstract

This is a doctoral thesis on the application of techniques originally developed in the programme of characterisation of supersymmetric solutions to Supergravity theories, to finding alternative backgrounds. We start by discussing the concept of a Killing spinor, and how these are paramount to the process of classifying the aforementioned supersymmetric solutions. Moreover, these geometric objects also have applications when considered in different scenarios (the 'beyond' in the title). In particular, techniques based on a different parallelising rule for a spinorial field can be used for obtaining solutions to Einstein-Maxwell-De Sitter theories, as well as a (partial) classification of lorentzian Einstein-Weyl manifolds, a problem of geometrical interest. The annexe contain an introduction and summary in Spanish language. The appendices discuss the tensorial and spinorial conventions employed, some relevant geometrical information on the scalar manifolds for the matter contents of interest, as well as for the null case solutions, including Kundt waves. Also, a short introduction to Weyl geometry and the Similitude group, as well as the Lorentz and Spin groups, is given.

Ph.D. thesis, IFT UAM/CSIC, June 2012 (v2: minor changes)

References in corpus (19)

• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Hidden supersymmetry of domain walls and cosmologies
• The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets
• Metrics With Vanishing Quantum Corrections
• Geometry of all supersymmetric type I backgrounds
• Hamilton-Jacobi method for Domain Walls and Cosmologies
• General Kundt spacetimes in higher dimensions
• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
• Supersymmetric solutions of N=2 d=4 sugra: the whole ungauged shebang
• Pseudo-supersymmetry and a Tale of Alternate Realities
• Supersymmetry, attractors and cosmic censorship
• Supersymmetric coloured/hairy black holes
• Geometry of four-dimensional Killing spinors
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• HKT Geometry and de Sitter Supergravity
• Geometry of all supersymmetric four-dimensional $\mathcal{N}=1$ supergravity backgrounds
• Supersymmetry, holonomy and Kundt spacetimes
• Supersymmetric isolated horizons in ADS spacetime