4-formas y Membranas: Desde el Potencial con Flujos hasta la Ciénaga

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 11-09-2020Esta tesis tiene embargado el acceso al texto completo hasta el 11-03-2022This thesis analyzes type II string compactifications, focusing both on the structure of the scalar potential and its relation to 3-forms and membranes and on exploring several Swampland Conjectures in this context. We begin by introducing some basic concepts of type II flux compactifications on Calabi-Yau (orientifolds). The corresponding moduli space is introduced and its structure is examined, giving some remarks on mirror symmetry, too. The flux induced superpotential is also reviewed. The structure of the perturbative flux-induced potential is the object of study of the second part of the thesis. We review its formulation for type IIA Calabi-Yau orientifolds in terms of 4-dimensional 3-forms. It is found that it enjoys a generalized Dvali-Kaloper-Sorbo structure, namely it can be obtained from the couplings between Minkowski 4-forms (with saxion-dependent kinetic terms) and shift invariant axion polynomials, which depend only on fluxes and axions. Moreover, we explain how the whole potential (including the terms coming form localized sources) can be written as a bilinear of the aforementioned polynomials, which can at the same time be further factorized into an axion dependent matrix and a flux vector. This structure is interpreted microscopically in terms of the preclusion of Freed-Witten anomalies (and the Hanany-Witten effect). We obtain a very simple relation between the superpotential and what we call the master axion polynomial. 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. In fact, it is shown how each of the different terms in the formula for the potential is in one-to-one correspondence with the exchange of 3-forms, scalars and gravitons between the membranes. Moreover, this correspondence turns out to be valid not only at the vacua of the potential, but also in the rest of field space. Finding the set of generic conditions that are fulfilled by every Effective Field Theory that can be embedded in QG is the goal of the Swampland program, and exploring this in the context of type II compactifications is the main point of the third part of this thesis. We begin by reviewing some Swampland Conjectures and then turn to the study of the Swampland Distance Conjecture for type II compactifications on a Calabi-Yau (orientifold), focusing on extended objects. We compute the masses and tensions of particles, strings and membranes arising from different Dp and NS5-branes wrapping supersymmetric cycles. The objects becoming massless or tensionless at different infinite distance points are classified, and consistency with mirror symmetry is checked, supporting the known result that further non-geometric objects are needed. Additionally, we construct the infinite monodromy orbits of membranes. Moreover, we investigate toroidal models and relate the previously found tensionless membranes with the Weak Gravity Conjecture and the prevention of higherform symmetries from becoming global at the infinite distance points. The gauge couplings going to zero at such points are identified and verified to correspond exactly to the 3-forms that couple to the tensionless membranes. We finish by examining Scale Separation in a particular class of type II compactifications on twisted tori. Taking into account the full 10-dimensional picture turns out to be crucial. In fact, the backreaction of the internal geometry is seen to modify the results from the naive 4-dimensional EFT, which appeared to violate the relevant conjectures, in the right way for them to be satisfie