Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system

Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semimicroscopic description in terms of $(1+1)$-dimensional theories, we discuss the emergence of $(2+1)$-dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge-invariant theory and using particle vortex duality.