Non-Abelian 3d Bosonization and Quantum Hall States

TL;DR

This paper explores non-Abelian bosonization dualities in 3D Chern-Simons-matter theories and demonstrates their equivalence in describing non-Abelian quantum Hall states, linking condensed phases and vortex excitations across dual theories.

Contribution

It introduces a broader class of non-Abelian bosonization dualities and applies them to analyze quantum Hall states in both bosonic and fermionic theories.

Findings

Bosonic vortices form non-Abelian quantum Hall states.

Filling of Landau levels maps between bosonic and fermionic theories.

Ground states are described by the same quantum Hall wavefunction.

Abstract

Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then explore the non-relativistic physics of these theories in the quantum Hall regime. The bosonic theory lies in a condensed phase and admits vortices which are known to form a non-Abelian quantum Hall state. We ask how this same physics arises in the fermionic theory. We find that a condensed boson corresponds to a fully filled Landau level of fermions, while bosonic vortices map to fermionic holes. We confirm that the ground state of the two theories is indeed described by the same quantum Hall wavefunction.