W-infinity Field Theories for the Edge Excitations in the Quantum Hall Effect

TL;DR

This paper reviews effective field theories for quantum Hall edge excitations, comparing multi-component Abelian models and minimal W-infinity models, highlighting their classifications, experimental confirmations, and differences in conformal properties.

Contribution

It provides a comparative analysis of Abelian and W-infinity models for quantum Hall edges, emphasizing their theoretical classifications and conformal field theory distinctions.

Findings

Both models classify quantum Hall universality classes.

Experiments confirm predictions common to both models.

Abelian theories are rational conformal field theories, W-infinity models are not.

Abstract

We briefly review these low-energy effective theories for the quantum Hall effect, with emphasis and language familiar to field theorists. Two models have been proposed for describing the most stable Hall plateaus (the Jain series): the multi-component Abelian theories and the minimal W-infinity models. They both lead to a-priori classifications of quantum Hall universality classes. Some experiments already confirmed the basic predictions common to both effective theories, while other experiments will soon pin down their detailed properties and differences. Based on the study of partition functions, we show that the Abelian theories are rational conformal field theories while the minimal W-infinity models are not.