Calogero-Sutherland model from excitations of Chern-Simons vortices

Abstract

We consider a large-N Chern-Simons theory for the attractive bosonic matter (Jackiw-Pi model) in the Hamiltonian, collective-field approach based on the 1/N expansion. We show that the dynamics of density excitations around the ground-state semiclassical configuration is governed by the Calogero or by the Sutherland Hamiltonian, depending on the symmetry of the underlying static-soliton configuration. The relationship between the Chern-Simons coupling constant $\l$ and the Calogero-Sutherland statistical parameter $\l_c$ signalizes some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.