This thesis addresses two aspects of string theory: the string landscape (based on [3]) and the swampland (based on [4]). After a review of these concepts, the first part of the thesis is dedicated to the Weak Gravity Conjecture (WGC), one of the several criteria that allow to distinguish between the swampland of effective field theories without a quantum gravity completion, and the landscape of healthy theories. We study how infrared consistency conditions of 3D (and 4D) effective field theories with massive scalars or fermions charged under multiple U(1) gauge fields can yield to bounds of the WGC type. In the regime where charge-independent contributions to higher-derivative terms in the action are sufficiently small, it is then possible to derive constraints on the charge-to...[ Read more ]

This thesis addresses two aspects of string theory: the string landscape (based on [3]) and the swampland (based on [4]). After a review of these concepts, the first part of the thesis is dedicated to the Weak Gravity Conjecture (WGC), one of the several criteria that allow to distinguish between the swampland of effective field theories without a quantum gravity completion, and the landscape of healthy theories. We study how infrared consistency conditions of 3D (and 4D) effective field theories with massive scalars or fermions charged under multiple U(1) gauge fields can yield to bounds of the WGC type. In the regime where charge-independent contributions to higher-derivative terms in the action are sufficiently small, it is then possible to derive constraints on the charge-to-mass ratios of the massive particles from requiring that photons propagate causally and have an analytic S-matrix. We thus find that the theories need to contain bifundamentals and satisfy a version of the weak gravity conjecture known as the convex-hull condition. Demanding self-consistency of the constraints under Kaluza-Klein compactification [5, 6], we furthermore show that, for scalars, they imply a stronger version of the weak gravity conjecture in which the charge-to-mass ratios of an infinite tower of particles are bounded from below. We find that the tower must again include bifundamentals but does not necessarily have to occupy a charge (sub-)lattice.

In the second part of the thesis, we focus on a statistical approach to the landscape and the embedding of Higgs-like physics. In particular, we work withing the racetrack Kähler uplift model in Type IIB flux compactifications, and the string theory landscape is generated by scanning over discrete values of all the flux parameters. We review how this model yields a statistical preference for an exponentially small vacuum energy Λ, that is the probability distribution P(Λ → 0) is particularly peaked. Then we observe that matching the median value of Λ to the observed one, a mass scale m ≃ 100 GeV naturally appears. We show how to slightly modify the model such that an Higgs-like scale can be identified with this mass scale.