Aspects of type IIA AdS$_4$ orientifold vacua

TL;DR

This thesis investigates the structure, stability, and uplift mechanisms of AdS4 vacua in type IIA flux compactifications, combining 4d effective theory analysis with 10d geometric considerations, including non-geometric fluxes and swampland conjectures.

Contribution

It provides a systematic search for SUSY and non-SUSY AdS4 vacua, analyzes their stability, and explores uplift scenarios to SU(3) and SU(3)×SU(3) manifolds beyond the smearing approximation.

Findings

Multiple families of SUSY and non-SUSY AdS4 vacua identified.

Some non-SUSY vacua are perturbatively stable and have scale separation.

D8 branes with D6 branes can satisfy decay conditions from the weak gravity conjecture.

Abstract

In this thesis we explore the vacua structure of type IIA orientifold (CY) compactifications with fluxes, from the 4d and the 10d point of view. We start by reviewing type IIA Calabi-Yau orientifold compactifications with fluxes. We consider RR and NSNS fluxes, and then add (non)-geometric fluxes. We recall how the potential can be written as a bilinear expression and review the main swampland conjectures involving these scenarios. Once the basics have been setted, we perform a systematic search of vacua, using directly the 4d action. We focus first on the case with RR and NSNS fluxes and then repeat the same game by including geometric fluxes. We find several families of SUSY and non-SUSY AdS$_4$ vacua. We check which of them are (perturbatively) stable and which have separation of scales. We then analyse from the 10d perspective the SUSY vacua derived in the 4d effective theory. We comment on how an uplift to $SU(3)$ structure manifolds does not exist unless the O6 planes are smeared. We go beyond this approximation and look for an uplift in $SU(3)\times SU(3)$ manifolds, considering only the case with RR and NSNS fluxes. To do so, we expand the equations of motion in terms of $g_s$. At zeroth order we recover the smearing approximation. We solve the expansion at first order, where the localised nature of the O6-planes is taken into account. We use the same machinery to study the non-perturbative stability of some of the families of non-SUSY vacua with only RR and NSNS fluxes. According to a refined version of the weak gravity conjecture, there should be membranes in the spectrum with $Q > T$, triggering its decay. We see that D8 branes wrapping the internal manifold with D6 branes ending on them can satisfy this requirement. We finish by recapping all the results and making some comments about which questions are still open.