Flux Backgrounds and Generalised Geometry
Examensarbete för masterexamen
In this thesis we study aspects of compactifications of mainly the type II supergravity theories. We begin with the study of classical approaches with a Kaluza-Klein compactification of the type II supergravity theories on a Calabi-Yau 3-fold, followed by a presentation of their orientifold variants, mirror symmetry, and the effects of allowing background fluxes on the moduli in the 4D effective field theory. The moduli fields can be stabilised by the presence of non-trivial background fluxes, perturbative corrections to the 10D theory and non-perturbative corrections to the 4D scalar potential. These corrections can be used to construct toy model de Sitter vacua as in the KKLT and large volume scenarios. We also introduce a compactification with so-called non-geometric fluxes, whose presence makes the metric of the internal manifold ill-defined. This is followed by a discussion of double field theory, which treats geometric and non-geometric fluxes on equal footing by extending spacetime in order to covariantise the T-duality group O(d, d). We briefly discuss consistent truncations in the context of the generalised Scherk- Schwarz ansatz. This is followed by an introduction of exceptional field theory, which is also an extension of supergravity which covariantises the exceptional U-duality groups. This brings us to the formalism of exceptional generalised geometry where we formulate supersymmetric flux backgrounds as torsion-free generalised G-structures. The notion of generalised G-structures is then interpreted as generalised differential forms in exceptional field theory and used to describe vacua. The application to find consistent truncations to 4D is also discussed. This construction is believed to play an important role in the classification of supersymmetric backgrounds.