A Fermionic Swampland Conjecture

In this thesis we study the Fermionic Weak Gravity conjecture in the context of gauged N = 2 supergravity in four dimensions. The rich geometrical structure of supergravity theories provides a natural way to realize constraints coming from a consistent completion to quantum gravity, and in this work we focus on a proposed inequality relating Yukawa couplings and the scale of supersymmetry breaking. We explore the conjecture on Minkowski vacua with broken supersymmetry, both in the general case and in explicit models. We find that some physically relevant parametric limits partially realize the inequality, while other regimes remain out of predictive reach. Explicit models also suggest that it might be crucial to fix the moduli, and we give a few ways in which this work might be extended in the future.