The purpose of this thesis is twofold and motivated by recent developments in string theory and extra dimensional models. The first objective is to describe the development and progress in the codimension-2 brane paradigm as a potential cosmological scenario. Secondly, it presents the Antide Sitter/Conformal Field Theory (AdS/CFT) conjecture, also known as holography, as a tool for calculating physical quantities in condensed matter system and goes on to model the quantum Hall effect. We first describe the initial development of treating back-reaction in codimension-2 branes systems with a scalar and gauge field. The purpose of this is to examine the low-energy effective dynamics on the brane. Furthermore, applications are then explored for D7-branes in F-theory as well as D3-branes in large extra dimensional scenarios explored as a model for the cosmological constant problem. The result of this work is that the higher and lower dimensional scenarios are consistent with each other once brane back-reaction is considered in these models. This work led to a number of future works one of which is in relation to the cosmological constant problem. While the subsequent work is beyond the scope of this thesis, we present a picture and further references for the reader. The larger, later, portion of this thesis introduces the concept of holography, its origins, and the applicability to condensed matter systems. Furthermore, we discuss the applicability in particular to the quantum Hall effect (QHE) and present a model in the holographic language that correctly reproduces some of the physics of the QHE. This includes a paper in which we introduce the model, along with demonstration of symmetry properties and conductivity calculations, as well as a paper which examines the finite size scaling behaviour of the model. As a benefit to the reader, we present a `starter edition guide' to the AdS/CFT dictionary preceding these papers for non-experts such that this thesis is self-contained. The upshot is that these avenues of work, in particular quantum Hall-ography, have been very successful in modeling physics using tools originally developed by string theory. As such, it provides support for string theory as a model and framework, as well as providing more opportunities for future predictions of physical quantities.

Doctor of Philosophy (PhD)