Generalized symmetries and symmetry topological field theory of 3-dimensional ABJ theories from string theory and branes

Understanding symmetries in quantum field theory is crucial for unraveling the fundamental principles that govern physical systems. Though less explored than ordinary symmetry, treading the path of generalized symmetries opens up new avenues for understanding complex phenomena. The goal of this thesis is to investigate these symmetries in 3-dimensional QFTs through the derivation of a bulk topological theory in one dimension higher that describes the discrete generalized symmetries of strongly coupled 3d ortho-symplectic ABJ (Aharony-Bergman-Jafferis) theories. In order to achieve this, the research will rely on holographic duality, established through AdS/CFT correspondence, which eases the investigation of non-perturbative phenomena by mapping a given strongly coupled d-dimensional QFTs to a weakly coupled gravitational theory in (d+1) dimensions. String theory, and in particular its low-energy limit (IIA supergravity), does in fact offer a useful framework for capturing symmetries through a topological limit or, better said, truncation. With a particular focus on the flux sector of supergravity and by using the discrete torsions of the holographic geometry in IIA, i.e. AdS_4 x CP^3/Z_2, we construct the 4-dimensional "Symmetry topological field theory (TFT)'' via compactification on the space, CP^3/Z_2. The resulting TFT then allows to identify generalized symmetries and anomalies of the original QFT in terms of couplings between branes, that are the fundamental extended dynamical objects of string theory. This thesis contributes to a deeper understanding of the nature of generalized symmetries in 3-dimensional QFTs and their connections to holography and string theory. Such knowledge can have implications in various fields, including condensed matter physics and topological phases of matter.