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

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