Particle-Vortex Duality from 3d Bosonization

TL;DR

The paper presents a simple, relativistic construction of 3d bosonization in $d=2+1$ via flux attachment, starting from a unit Chern-Simons coupling to transmute statistics and connect bosonic and fermionic theories. From this seed, it derives a broad web of dualities, including bosonic and fermionic particle-vortex dualities, time-reversal variants, self-dual theories, and a vortex–vortex duality, all organized through BF and CS couplings and careful flux quantization. It also discusses non-Abelian extensions, supersymmetric analogs, and RG-flow perspectives, arguing for a unifying viewpoint that particle-vortex duality effectively constitutes a squared form of bosonization. The results provide cross-checks via monopole operator quantum numbers and current correlator equivalences, with potential applications to condensed matter and holographic contexts. Overall, the work offers a coherent, constructive framework to generate and test Abelian dual pairs in 3d and to explore their supersymmetric and non-Abelian generalizations.

Abstract

We provide a simple derivation of particle-vortex duality in d=2+1 dimensions. Our starting point is a relativistic form of flux attachment, designed to transmute the statistics of particles. From this seed, we derive a web of new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.