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Over the years, many theoretical frameworks have been developed to understandthe remarkable physics of the quantum Hall system. In this work we discuss theinterplay among quantum wires, Chern-Simons theory, bosonization, andparticle-vortex duality, which enable a unified approach for the Laughlinstates of the fractional quantum Hall system. Starting from the so-calledquantum wires system, which is a semi-microscopic description in terms of 1+1dimensional theories, we discuss the emergence of 2+1 dimensional low-energyeffective field theories by using different maps connecting the microscopicdegrees of freedom with the macroscopic ones. We show the origin of these mapsby embedding the bosonized version of the original quantum wires model in agauge invariant theory and using particle vortex-duality.

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