TL;DR
This paper provides a comprehensive overview of dualities in 2+1 dimensions, covering Abelian and non-Abelian cases, their connections to supersymmetry, lattice models, large N theories, and applications to quantum Hall physics.
Contribution
It offers a detailed synthesis of dualities in 2+1 dimensions, including new insights into their interrelations and applications in condensed matter and high-energy physics.
Findings
Unified framework for Abelian and non-Abelian dualities
Connections between dualities and supersymmetry
Application to quantum Hall effect
Abstract
In this course, we will discuss dualities in 2+1 dimensions. We begin by briefly reviewing the physics of 1+1d T-duality and bosonization, and discuss flux attachment and the dual photon in 2+1d. Then, we introduce 2+1d particle-vortex duality, bosonization and their associated web of dualities. This includes discussing more elaborate Abelian dualities, including self-dual theories and quiver theories. Next, we move on to non-Abelian physics, discussing QCD in three dimensions and more. This done, we will discuss the relation of these dualities to SUSY dualities, lattice physics, and large N physics; and finally, we present the application of one of the Abelian dualities to quantum Hall physics. These lecture notes are expanded from lectures delivered at XIV Modave Summer School in Mathematical Physics in September 2018.
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