4-Forms and Membranes: From the Flux Potential to the Swampland

This thesis explores different aspects of type II string compactifications. In the first part, we will focus on the structure of the perturbative flux-induced scalar potential. We will describe how it can be explained in terms of 3-forms coupling to shift-invariant axion polynomials, and show that this implies a bilinear structure in those polynomials. The shift-invariant polynomials will also be interpreted microscopically in terms of the preclusion of Freed-Witten anomalies, and the relation between the superpotential in the N=1 formulation and the so-called master axion polynomial will be explained. Motivated by this structure of the potential in terms of 3-forms, which couple naturally to (codimension 1) membranes, we propose a correspondence between the 4-dimensional F-term N = 1 scalar potential and a system of parallel BPS membranes, which is satisfied even off-shell. In the second part, we will explore some Swampland conjectures in type II compactifications. We will begin by exploring the Swampland Distance Conjecture focusing on membranes, and characterising the subset of them that become tensionless at infinite distance points. We will furthermore explore their associated energy scales, together with those of particles and strings in a particular toroidal model, and relate the previously found tensionless membranes with the Weak Gravity Conjecture and the prevention of higher-form symmetries from becoming global at the infinite distance points. We finish by examining Scale Separation in a particular model that apparently violates the AdS Distance Conjecture. We will show that taking into account the full 10d backreacted solution crucially modifies the naive 4d EFT in the precise way for the conjecture to be satisfied.