String Vacua and the Swampland

The swampland program, initiated by C.Vafa in 2005, aims at extracting the subset of apparently consistent low-energy effective field theories coupled to gravity which can be UV-completed. To this end, a complicated web of intertwined conjectures has been developed. The so-called swampland conjectures are conditions that are supposed to be satisfied whenever a theory admits a completion to quantum gravity and should be satisfied trivially when a theory decouples from gravity. In practice, the conjectures derive support either by string theoretical setups or by microscopic arguments. The implications of the swampland program for string phenomenology are far-reaching, rendering for example several inflation models inadmissible. The de Sitter conjecture forbids all de Sitter vacua, pointing towards scenarios of time-dependent cosmological constant, such as quintessence. The more recently proposed trans-Planckian censorship conjecture (TCC) allows for de Sitter vacua, as long as they are short-lived enough. The aim of this thesis is to better understand the part of the swampland program that directly concerns the allowed vacua. We could say that this is a three-fold task, consisting of the subgoals of properly understanding the validity regimes of the relevant conjectures, identifying possible interrelations, and finally extracting the not-so-obvious implications of them. In fact, we start by examining two conjectures relevant for AdS vacua, namely the AdS distance and the AdS scale separation conjecture. Analyzing the prominent KKLT and LVS constructions, which exploit quantum effects to achieve moduli stabilization, we propose that they should receive appropriate logarithmic quantum corrections. Assuming in turn that the dS conjecture also receives similar corrections, we find that their implications align nicely with TCC. In addition, we investigate the consequences of the dS conjecture for non-BPS branes. Observing that in certain setups a single non-BPS brane is sufficient to violate the conjecture, we argue that the K-theory charge on a compact space should cancel