In has become clear in recent years that working in sectors of large global charge of strongly coupled and otherwise inaccessible CFTs leads to important simplifications. It is indeed possible to formulate an effective action in which the large charge appears as a control parameter. In this talk, I will explain the basic notions of the large-charge expansion using the simple example of the O(2) model and then generalize to models with a richer structure which showcase other effects. [For the zoom link please email alejandro.cabo_bizet@kcl.ac.uk]

The large-charge approach consists in studying conformal field theories in sectors of fixed and large global charge. This allows performing a perturbative expansion of a generically strongly-coupled theory with the inverse charge acting as a controlling parameter. In this talk, I will present the basic idea of the large-charge expansion using the simplest example of the 3D O(2) model at the Wilson-Fisher fixed point, as well as its application to other models.

In the moduli stabilization program a la KKLT, the dilaton and the complex structure moduli are fixed via background 3-form fluxes, whereas the Kaehler moduli are fixed through non-perturbative effects such as Euclidean D3-brane instantons and gaugino condensation. After briefly introducing toroidal orbifolds, I will discuss some issues of stability and then turn to moduli stabilization in resolved toroidal type IIB orientifolds. The main emphasis will be on the resolution of the singularities via blow-ups, gluing together the local patches to obtain a smooth Calabi-Yau, and the topologies of the exceptional divisors.