Particle-Vortex Duality from 3D Bosonization

Abstract

We show how particle-vortex duality in $d$ = 2 + 1 dimensions arises as part of an intricate web of relationships between different field theories. The starting point is “bosonization,” a conjectured duality that uses flux attachment to transmute the statistics of relativistic particles. From this seed, we derive many old and new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.