Aspects of flux compactification

In this thesis, we study three main aspects of flux compactifications: (1) classify supergravity solutions from flux compactification; (2) construct flux-deformed geometry and 4D low-energy theory to describe these flux vacua; and (3) study 4D particle phenomenology and cosmology of flux vacua. In the first part, we review G-structure, the basic tool to study supersymmetric flux solutions, and some typical solutions obtained in heterotic, type IIA and type IIB string theories. Then we present a comprehensive classification of supersymmetric vacua of M-theory compactification on 7D manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have [special characters omitted] = 1, 2, 3, 4 supersymmetry and the internal space allows for SU(2)-, SU(3)- or G 2-structures. In particular, we find for [special characters omitted] = 2 supersymmetry, that the external space-time is Minkowski and the base manifold of the internal space is conformally Kähler for SU(2) structures, while for SU(3) structures the internal space has to be Einstein-Sasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with [special characters omitted] = 1 supersymmetry and SU(3) structure, where all fluxes are non-zero and the first order differential equations are solved. In the second part, we simply review the methods used to construct one subclass of fluxed-deformed geometry or the so-called twisted manifold , and the associated 4D effective theory describing these flux vacua. Then by employing (generalized) Scherk-Schwarz reduction, we construct the geometric twisting for Calabi-Yau manifolds of Voisin-Borcea type (K 3 × T2)/[special characters omitted] and study the superpotential in a type IIA orientifold based on this geometry. The twists modify the direct product by fibering the K 3 over T2 while preserving the [special characters omitted] involution. As an important application, the Voisin-Borcea class contains T6/([special characters omitted] × [special characters omitted]), the usual setting for intersecting D6 brane model building. Past work in this context considered only those twists inherited from T6, but our work extends these twists to a subset of the blow-up modes. In the last part, we discuss the connection of flux vacua to the phenomenology of particle physics. In particular, we study the compatibility conditions between particle physics phenomenology and flux background, and the embedding of the stringy particle physics models into some flux vacua on type IIB T6/([special characters omitted] × [special characters omitted]) orientifolds. The associated phenomenology of these models with fluxes turned on are also discussed. We end up this discussion with some comments on model building in type IIA flux vacua