Fractional Quantum Hall Effect from Anomalies in WZNW Model

TL;DR

This paper explores the Fractional Quantum Hall Effect through anomalies in a WZNW model, linking edge theories and non-Abelian bosonisation to explain quantized conductivities.

Contribution

It introduces a unified approach using anomalies in WZNW models to describe both integer and fractional quantum Hall effects.

Findings

WZNW theory captures quantization of conductivities

Edge anomalies relate to FQHE and IQHE

Unified description of quantum Hall effects

Abstract

An approach to understand Fractional Quantum Hall Effect (FQHE) using anomalies is studied in this paper. More specifically, this is done by looking at the anomaly in the current conservation equation of a WZNW theory describing fields living at the edge of the two dimensional Hall sample. This WZNW theory itself comes from the non-Abelian bosonisation of fermions living at the edge. It is shown that this model can describe both integer and fractional quantization of conductivities in a unified manner.