On de Sitter string vacua in the Large Volume Scenario

Purpose of this thesis is to analyze certain aspects of the presence of de Sitter space in type IIB string compactifications. It focuses, in particular, on the mechanism based on the introduction of an anti-D3-brane at the tip of a warped throat of the compact space, which under certain conditions allows to stabilize all the moduli at a de Sitter minimum of their scalar potential. The first part is a review of the background material used in this work. It starts with an introduction to string compactification on a Calabi-Yau three-fold, which is followed by the description of the main techniques that are used to stabilize all the (complex structure and Kahler) moduli arising in such compactification. Then, it presents the problem of finding de Sitter minima in string theory and the main proposals to address it, with a specific focus on the method based on anti-D3-branes and on the issues related to the D3-tadpole cancellation condition, which is one of the main aspects analyzed in the thesis. Finally it reviews several important topics which are important for the construction of explicit models in string theory. The second part contains my original research work. First, we construct and analyze an explicit model in the frame of the Large Volume Scenario, in which all the moduli can be consistently stabilized in a de Sitter minimum. We also list a set of important requirements that need to be fulfilled in order to have a consistent solution in which all the approximations are under control and we analyze them in the context of the class of models under consideration. After that, we perform a statistical analysis of the distribution of the D3-charge for models with several Kahler moduli (up to 12) and we stress the important role of the D7-brane configuration known as Whitney brane (already used in the explicit construction mentioned before) in relation to the D3-tadpole cancellation condition. Finally, we provide an additional explicit construction in which, with respect to the first one, we add the requirement of having a K3 fibration, a configuration which is more promising from the phenomenological point of view.