The landscape of String Theory (ST) is believed to be made of 10^(500) vacua, having some of them properties that are similar to those of our Universe. The existence of these vacua can explain some of the hardest problems in Cosmology and High Energy Physics: the cosmological constant problem, the hierarchy problem, and the almost-flatness of the inflation potential.

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Compactification from 10 to 4 dimensions

To give a description of our Universe from ST, we need to do a compactification from 10 to 4 dimensions. Depending on the choice of the internal 6D geometry, our Universe will exhibit different properties. Recently, some examples of de Sitter (dS) universe (the one that resembles our Universe) have been obtained from non-geometric flux compactification.

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Non-geometric Flux Compactification

Within the space of possible solutions, one expects that the ST landscape should be mostly populated by non-geometric backgrounds. However, despite of their relevance, some important questions about non-geometric flux compactification are still unknown. One reason people focused more on geometric backgrounds is because they are technically more under control than the non-geometric ones.

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Weak Gravity and Ooguri-Vafa Conjectures

In this project we want to test and use the Weak Gravity (WGC) and the recent Ooguri-Vafa conjectures (OVC) on the vacua solutions of gauged SUGRAs with alpha' corrections. These conjectures provide a principle to rule out the vacua that do not have a stringy origin and belong to the "swampland". To do so, we propose two strategies.

Double/Exceptional Field Theories

Firstly, Double/Exceptional Field Theories (DFT/EFT) give a criterion to distinguish the lower dimensional supergravities (SUGRAs) that have a (non-)geometric origin. We will make use of these duality symmetric theories to classify the arena of (non-)geometric vacua. The recent progress on the alpha'-corrected DFT and gauged SUGRAs will allow us to study the stability of these vacua.

Vacua Structure of Type II Supergravity Theories

Secondly, we will consider the vacua structure of the compactification of type II supergravity theories when brane sources are considered. These constructions, which circumvent the no-go type theorems on the existence of de Sitter universes, will potentially provide an unexplored plethora of vacua. In this direction, having a duality symmetric formulation of supergravity theories containing quantum corrections, will allow us to test the aforementioned conjectures with a very high precision.

Summary

In summary, a very extensive exploration needs to be done to determine how much of the ST landscape, if any, is made of honest-to-goodness ST solutions, thus resolving the question of their consistency. If most of the candidate vacua do not survive consistency and stability checks, the landscape would be drastically pruned. This in turn would greatly weaken the multiverse paradigm in favor of a theory of everything paradigm, and reinforce the quest for predictability in ST.