8 research outputs found
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 in a purely algebraic and algorithmic way, where is a left-invariant homomorphism. Specialising this
to the case of symmetric M-theory backgrounds (i.e. with a
symmetric space and 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