The homogeneity theorem for supergravity backgrounds II: the six-dimensional theories

We prove that supersymmetry backgrounds of (1,0) and (2,0) six-dimensional supergravity theories preserving more than one half of the supersymmetry are locally homogeneous. As a byproduct we also establish that the Killing spinors of such a background generate a Lie superalgebra.Comment: 16 page

The homogeneity theorem for supergravity backgrounds

We prove the strong homogeneity conjecture for eleven- and ten-dimensional (Poincar\'e) supergravity backgrounds. In other words, we show that any backgrounds of 11-dimensional, type I/heterotic or type II supergravity theories preserving a fraction greater than one half of the supersymmetry of the underlying theory are necessarily locally homogeneous. Moreover we show that the homogeneity is due precisely to the supersymmetry, so that at every point of the spacetime one can find a frame for the tangent space made out of Killing vectors constructed out of the Killing spinors.Comment: 8 page

(M-theory-)Killing spinors on symmetric spaces

We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow \Lambda^*(TM)$ is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e. $(M,g,F)$ with $(M,g)$ a symmetric space and $F$ an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.Comment: Updated abstract for clarity. Added missing geometries to section 6. Main result stand

Homogeneity in supergravity

This thesis is divided into three main parts. In the first of these (comprising chapters 1 and 2) we present the physical context of the research and cover the basic geometric background we will need to use throughout the rest of this thesis. In the second part (comprising chapters 3 to 5) we motivate and develop the strong homogeneity theorem for supergravity backgrounds. We go on to prove it directly for a number of top-dimensional Poincaré supergravities and furthermore demonstrate how it also generically applies to dimensional reductions of those theories. In the third part (comprising chapters 6 and 7) we show how further specialising to the case of symmetric backgrounds allows us to compute complete classifications of such backgrounds. We demonstrate this by classifying all symmetric type IIB supergravity backgrounds. Next we apply an algorithm for computing the supersymmetry of symmetric backgrounds and use this to classify all supersymmetric symmetric M-theory backgrounds