Chiral bosons on Bargmann space associated with A$_r$ Statistics

TL;DR

This paper studies a system of particles obeying A_r statistics, showing that its edge excitations can be described by a tensor product of abelian chiral bosons, generalizing Wess-Zumino-Witten theory.

Contribution

It introduces a novel description of edge excitations for A_r statistical systems using a tensor product of abelian bosonic fields within a chiral boson framework.

Findings

Edge excitations are described by a tensor product of r abelian bosonic fields.

The system's bulk behaves as a quantum droplet with a constant Husimi distribution.

Quantization of the edge dynamics is achieved using Fock-Bargmann representations.

Abstract

We consider a large collection of particles obeying $A_r$ statistics. The system behaves like a quantum droplet characterized by a constant Husimi distribution. We show that the excitations of this system live on the boundary of the droplet and they are described by an effective chiral boson action generalizing the Wess-Zumino-Witten theory in two dimension. Our analysis is based on the Fock-Bargmann analytical representations associated to $A_r$ statistics. The quantization of the theory describing the dynamics on the edge is achieved. As by product, we prove that the edge excitations are given by a tensorial product of $r$ abelian bosonic fields.