Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction

TL;DR

This paper explores the quantum fluctuations in a large-N Chern-Simons theory with bosonic matter, revealing a connection to the Sutherland model and indicating a form of statistical transmutation linked to dimensional reduction.

Contribution

It demonstrates the equivalence of low-lying excitations in the Chern-Simons model to the Sutherland model and uncovers a relationship between coupling constants suggesting statistical transmutation.

Findings

Low-lying density excitations match the Sutherland model dynamics.

The coupling constant relationship indicates statistical transmutation.

Dimensional reduction is associated with changes in statistical parameters.

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 lambda_s signalizes some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.