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 $ł$ and the Calogero-Sutherland statistical parameter ${ł}_c$ signalizes some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.

revtex, 11 pages. The delta interaction included, as required by latest results on renormalization of the Chern-Simons theory. This does not change the conclusion of the paper

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