Dualities, extended geometries and the string landscape

This thesis is concerned with the role of dualities and nongeometric backgrounds in string theory. Dualities define nontrivial mappings by which seemingly distinct theories can be identified as alternative descriptions of the same physical reality. Their presence often suggests that the dual models are built upon more fundamental structures which cannot be fully captured by the applied formalisms. In string theory the web of dualities between the five consistent superstring theories served as a motivation to postulate the existence of an underlying M-theory. However, it was later observed that certain background fluxes are thereby mapped to objects which are ill-defined in conventional differential geometry. Such nongeometric backgrounds play an essential role in the field of string phenomenology. The first half of this work focuses on the application of extended field theories to describe string theories on generalized backgrounds. An emphasis is thereby placed on dimensional reductions of type II double field theory, which allows for a local description of type II supergravities with geometric and nongeometric fluxes. We show explicitly by the examples of Calabi-Yau manifolds and K3 × T${}^2$ that the effective four-dimensional action of such models is described by gauged supergravities in which all appearing moduli are stabilized. The role of the fluxes in respect of the structure of the effective action and the relation to other approaches to flux compactifications are discussed in detail. The second half of this thesis is built around the statistical analysis of string vacua in orientifold compactifications with fluxes. A major focus is thereby set on the interplay between dualities and the so-called tadpole-cancellation condition. We demonstrate at the example of T${}^6$/$Z_2$ × $Z_2$ that only a small fraction of the computed vacua is located in a region for which both a perturbative approach and a probe approximation for D-branes are reliable. In addition, we show that the vacua often accumulate on submanifolds of the full moduli space and that there exist certain voids in which no values are stabilized under the given assumptions. The issues of moduli stabilization and model building are therefore closely intertwined, and a unified treatment might provide valuable insights into the structure of the string landscape.