On F-theory effective actions: From anomalies to Swampland

Abstract

In this thesis we investigate general properties of four- and six-dimensional effective actions with minimal supersymmetry obtained from F-theory by compactification on Calabi-Yau manifolds. More specifically, we analyze the 4d N=1 gauge coupling functions and their one-loop corrections, we show the cancellation of chiral anomalies in four and six dimensions when the F/M-theory duality can be utilized and finally we provide yet another strong piece of evidence for the Swampland Distance Conjecture in the context of string theory, by testing it in the K\"ahler moduli spaces of Calabi-Yau threefolds. Along the way, we perform the reduction of M-theory on a Calabi-Yau fourfold in full generality, study in great detail the behaviour of anomalies under circle compactifications, settle the F-theory lift to six-dimension and provide further evidence for the relationships between the Swampland Distance Conjecture, the emergence proposal and the absence of global symmetry.