Aspects of string theory compactifications: D-brane statistics and generalised geometry

In this thesis two different aspects of string theory
compactifications are investigated. The first part deals with the
issue of the huge amount of possible string vacua, known as the
landscape. Concretely we investigate a specific well defined subset
of type II orientifold compactifications. We develop the necessary
tools to construct a very large set of consistent models and
investigate their gauge sector on a statistical basis. In
particular we analyse the frequency distributions of gauge groups
and the possible amount of chiral matter for compactifications to
six and four dimensions. In the phenomenologically relevant case of
four-dimensional compactifications, special attention is paid to
solutions with gauge groups that include those of the standard
model, as well as Pati-Salam, SU(5) and flipped SU(5) models.
Additionally we investigate the frequency distribution of coupling
constants and correlations between the observables in the gauge
sector. These results are compared with a recent study of Gepner
models. Moreover, we elaborate on questions concerning the
finiteness of the number of solutions and the computational
complexity of the algorithm. In the second part of this thesis we
consider a new mathematical framework, called generalised geometry,
to describe the six-manifolds used in string theory
compactifications. In particular, the formulation of T-duality and
mirror symmetry for nonlinear topological sigma models is
investigated. Therefore we provide a reformulation and extension of
the known topological A- and B-models to the generalised framework.
The action of mirror symmetry on topological D-branes in this setup
is presented and the transformation of the boundary conditions is
analysed. To extend the considerations to D-branes in type II
string theory, we introduce the notion of generalised calibrations.
We show that the known calibration conditions of supersymmetric
branes in type IIA and IIB can be obtained as special cases.
Finally we investigate the action of T-duality on the generalised
calibrations.