Moduli Stabilization and Stability in Type II/F-theory fux compactifcations

• Autores: David Prieto Rodríguez
• Directores de la Tesis: Fernando G. Marchesano Buznego (dir. tes.)
• Lectura: En la Universidad Autónoma de Madrid ( España ) en 2023
• Idioma: inglés
• Número de páginas: 377
• Títulos paralelos:
  • Estabilización de módulos y estabilidad en vacíos con flujos de las teorías Tipo II / Teoría-F
• Enlaces
  • Tesis en acceso abierto en: Biblos-e Archivo
• Resumen

  • In this thesis we study String Theory compactifcations to four dimensions focusing on the moduli stabilization process and the associated vacua structure in various frameworks, from Type IIA to F-theory. We interpret the results in the context of the Swampland Program. We start with a basic introduction to String Theory and the Swampland conjectures to lay out all the ingredients used throughout the thesis. We also summarize the geometrical aspects of Calabi-Yau orientifolds and their role in massive Type IIA compactifcations. We end the review with a discussion on the current state of the feld, presenting the approximated 10d solutions to the equations of motion with fuxes and the bilinear formalism of the 4d efective potential created by the RR and NSNS fux quanta. Having introduced all the key concepts and background results, we generalize the bilinear formalism of the scalar potential to include the contributions of geometric and non-geometric fuxes, which is later used to perform a systematic search of vacua. Using an Ansatz motivated by the goal of achieving stable de Sitter vacua, we study the equations of motion of Type IIA with metric fuxes. We obtain only AdS vacua, both SUSY and non-SUSY, checking their stability and generalizing several results from the literature. We try to fnd scale separation but fail to do so for generic solutions. We also consider the 10d uplift of AdS4 vacua arising from the 4d massive Type IIA efective theory with only RR and NSNS fuxes. Using the language of SU(3) × SU(3) structures and performing an expansion around the smearing approximation in powers of the string coupling, we study the stability of the supersymmetric solution and its nonsupersymmetric partner (associated with the former by a change of sign in the RR 4-form feld strength fux). We contrast the results with the Weak Gravity Conjecture and the AdS instability conjecture in several toroidal orbifold examples and fnd that some nonsupersymmetric cases are in tension with the predictions of those conjectures, hinting at the existence of additional corrections that have not been taken into account. After briefy introducing F-theory and Type IIB compactifcations, we study moduli stabilization in the complex structure sector of F-theory compactifcations over elliptically fbered Calabi-Yau 4-folds in the limit of Large Complex Structure. Using homological mirror symmetry, we are able to replicate the analysis for the Type IIA case and give a bilinear expression for the scalar potential, allowing for a simpler and more detailed study of the vacua structure. In the process, we fnd two distinct families of fux confgurations compatible with the tadpole constraints that allow for full moduli stabilization. The frst one requires polynomial corrections to fx all the moduli and the fux contribution to the tadpole scales with the dimension of the moduli space. In contrast, in the second family, polynomial corrections are not needed and only a pair of fuxes enters the tadpole independently of the number of moduli. We thoroughly examine the former in the Type IIB limit, where the superpotential is also quadratic and polynomial corrections can be considered at all orders. We argue that vacua fall into three classes depending on the choice of fux quanta. In particular, we provide analytic expressions for the vacuum expectation values and fuxinduced masses of the axio-dilaton and complex structure felds in a large subclass of vacua, independently of the Calabi-Yau and the number of moduli. Finally, we show that at this level of approximation supersymmetric vacua always contain fat directions