Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model

TL;DR

This paper explores quantum Hall droplets on complex projective spaces with mixed magnetic fields, deriving an effective edge theory described by a higher-dimensional, gauged WZW model, extending previous abelian-only analyses.

Contribution

It introduces a generalized higher-dimensional gauged WZW model as the effective edge theory for quantum Hall droplets with combined magnetic backgrounds.

Findings

Effective action is a chiral, gauged WZW theory in higher dimensions.

Generalization from abelian to nonabelian magnetic backgrounds.

Extension of edge state analysis to complex projective spaces.

Abstract

We consider quantum Hall droplets on complex projective spaces with a combination of abelian and nonabelian background magnetic fields. Carrying out an analysis similar to what was done for abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess-Zumino-Witten (WZW) theory generalized to higher dimensions.