Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball

TL;DR

This paper develops an effective Wess-Zumino-Witten action for edge states in higher-dimensional quantum Hall systems on the Bergman ball, using group theory and coherent states to analyze Landau levels and edge excitations.

Contribution

It introduces a generalized Wess-Zumino-Witten action for quantum Hall edge states on the Bergman ball, extending previous models to higher dimensions with a group-theoretic approach.

Findings

Wavefunctions as SU(k,1) coherent states

Construction of star product and density matrix

Formulation of effective edge state action

Abstract

Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball {\bf B}^k. This can be done by considering a system of particles living on {\bf B}^k in the presence of an uniform magnetic field B and realizing the ball as the coset space SU(k,1)/U(k). In quantizing the theory on {\bf{B}}^k, we define the wavefunctions as the Wigner \cal{D}-functions satisfying a set of suitable constraints. The corresponding Hamiltonian is mapped in terms of the right translation generators. In the lowest Landau level, we obtain the wavefunctions as the SU(k,1) coherent states. This are used to define the star product, density matrix and excitation potential in higher dimensions. With these ingredients, we construct a generalized effective Wess-Zumino-Witten action for the edge states and discuss their nature.