Landau-Ginzburg Theories for Non-Abelian Quantum Hall States

TL;DR

This paper develops Landau-Ginzburg effective field theories for non-Abelian fractional quantum Hall states, providing a new framework to understand their quasiparticle statistics and edge physics.

Contribution

It introduces a Meissner construction for non-Abelian Chern-Simons theories, linking bulk theories to edge coset constructions for non-Abelian quantum Hall states.

Findings

Constructed Landau-Ginzburg theories for non-Abelian states like Pfaffian.

Demonstrated how quasiparticle non-Abelian statistics emerge.

Connected bulk theories to edge coset models.

Abstract

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states -- such as the Pfaffian state -- which exhibit non-Abelian statistics. These theories rely on a Meissner construction which increases the level of a non-Abelian Chern-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping Abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor $\nu=1$, where the non-Abelian symmetry is a dynamically-generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-Abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories -- where a coset construction plays the role of the Meissner projection -- and discuss extensions to other states.