Over the past decades, string theory has emerged as a viable candidate for a ultra-violet (UV) complete theory of quantum gravity. In essence, by assuming that the fundamental objects of nature are 1-dimensional vibrating objects, it unifies an infinite number of fields in abstract spaces of dimension 10. In the process of relating string theory to our observed 4-dimensional Universe, the theory becomes inherently entangled with compact geometries, i.e., higher dimensional generalisations of spheres in the context of so-called string compactifications. That is, the theory needs to be reduced on a compact 6-dimensional manifold X by expanding fields into Fourier modes and keeping only the lightest degrees of freedom. Although challenging, the requirement for reducing the theory on a compact space gives a brilliant way of thinking about the unification of forces.


Depending on the perspective, the existence of extra dimensions can be viewed as a blessing or a curse. The plethora of degeneracies involved in making the theory effectively 4-dimensional gives rise to a colossal string theory landscape of valid EFTs, only one of which is believed to describe our Universe. Estimates on its size range from 10500 to 10272,000 with each solution characterising a distinct universe. It is the result of a great number of massless scalar fields, called moduli, characterising the size and shape of X. Mathematically speaking, they are associated with variations of the Kähler and complex structure of X at every point in the four non-compact dimensions. Since they would lead to unwanted observable long-range effects in 4D, they must gain large masses due to a dynamically generated potential. This procedure is conveniently referred to as moduli stabilisation.


Having proper control over quantum effects in string theory is typically a requisite for tackling issues related to moduli stabilisation. Because the physics in 4-dimensional spacetime is highly affected by procedure’s outcome, these challenges are of utmost importance for addressing phenomenological questions in string theory. In recent years, three procedures to generating de Sitter vacua in string theory with fully stabilised moduli have been established going by the names of KKLT, LVS and Kähler uplift.