Non-invertible continuous global symmetries and their symmetry theory from type II string theory

Generalized global symmetries are ubiquitous in quantum field theory (QFT) models, which describe the physics of particle interactions or low-energy matter phases. The generalization comes from extending the notion of charge conservation to the existence of topological (extended) operators in the theory. Generalized symmetries are important because they provide extra selection rules, which have been ignored until very recently. Non-invertible symmetries, which do not form a mathematical group, are one of such generalizations. For instance, they are present in Maxwell theory, Maxwell theory coupled to axions, and quantum electrodynamics (QED). They can be of discrete and finite type or of continuous type. The goal of this thesis is to systematically derive the non-invertible symmetries structure of 4d and 3d field theories constructed from type II string theories. The symmetry structure of a given QFT is encoded by another field theory (Symmetry Theory) defined on a space, which has an extra dimension.The physical QFT lives at the boundary of the symmetry theory. The study of the topological operators in the bulk symmetry theory and how they behave, depending on the choice of boundary condition, provides the full symmetry structure. The thesis consists of studying type II string theories backgrounds and implementing a dimensional reduction to derive the symmetry theory. The explicit backgrounds are provided by a Calabi-Yau geometry called the Conifold and the product manifold consisting of the Conifold times a circle.