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An outstanding problem in physics is to find a unified framework for quantum mechanics and general relativity. This is required for a better understanding of black holes and the early cosmology of the universe. String theory provides such a unification. In this thesis, we study aspects of compactifications of type IIB string theory. In the first part of the thesis, we study four-dimensional black holes consisting of D3-branes wrapping cycles in the compact dimensions. We discuss the correspondence between these black holes, topological string theory and matrix models. We then study the influence of black holes on the stability of flux compactifications. In the second part of the thesis, we turn to investigations of the type IIB landscape, i.e. the collection of stable and metastable vacua obtained from flux compactifications on conformal Calabi-Yau manifolds. We show that monodromies are important for the topographic structure of the landscape. In particular we find that there are long series of continuously connected vacua in the complex structure moduli space of the internal manifold. We also use geometric transitions to connect the moduli spaces of different manifolds, and create longer series of vacua. Finally, we investigate the stability of string theory vacua by constructing semiclassical instantons. These results have implications for the population of the landscape by eternal inflation.

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<p>This thesis reviews the theory of group extensions, gerbes and twisted K-theory. Application to anomalies in gauge theory is briefly discussed. The main results are presented in two appended scientific papers. In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension. In the second paper we introduce the fractional loop group L_qG, construct highest weight modules for the Lie algebra and discuss an application to twisted K-theory on G.</p>

Thesis--Ph. D., University of Hong Kong, 1981.

published_or_final_version / Physics / Master / Master of Philosophy

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