The magnetic weak gravity conjecture, the quantum gravity cut off and simple type IIA compactifications

The magnetic weak gravity conjecture (MWGC) imposes constraints on the maximum value of the cutoff associated with a gravitational Effective Field Theory. In its original formulation, the MWGC only included the gravitational and U(1) gauge interaction. One of the main goals of this thesis is to study the MWGC in the presence of scalar fields. We start by studying a general bosonic action describing a source interacting with three kinds of fields: scalar, gravitational, and U(1) gauge field. We continue looking for from the equations of motion and from them we obtain the so-called no-force condition, in the presence of these three interactions. We review the theory behind magnetic monopoles which together with the aforementioned condition help us extracting the generalization of the MWGC in the presence of scalar fields. Furthermore, we explore the interplay between the Distance Conjecture and the extension of the no-force condition. In the second part of the thesis, we review the theory behind compactifications, paving the way for a focused study of Type IIA compactification on a toroidal orbifold. We extract the spectrum of four-dimensional particles and strings arising from Dp-branes wrapping the corresponding cycles. The spectrum strictly depends on the Kähler moduli. We apply the extension of the MWGC for both particles and strings in various large volume limits, and after a review and computation of the species scale, we compare these three cutoffs. We show that the smaller cutoff, which means the first one to affect our theory, is the one associated with particles arising from D6-branes wrapping 6-cycles; which corresponds to the heaviest magnetic monopole. In this context, we finally introduce and test the so-called Distant Axionic String Conjecture, which relates the mass of the lightest tower near an infinite distance limit to the tension of an axionic string that dynamically drives the moduli towards that limit. Our results tells us something new.