Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction
Ivan Andric, Velimir Bardek, Larisa Jonke
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 low-lying density excitations around the ground-state vortex configuration is equivalent to that of the Sutherland model. The relationship between the Chern-Simons coupling constant lambda and the Calogero-Sutherland statistical parameter lambdas signalizes some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.
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