Duality and universality for the Chern-Simons bosons

By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg theory in 2+1 dimensions to the three-dimensional (3D) lattice Villain x-y model coupled with the Chern-Simons gauge field, we investigate phase transitions of Chern-Simons bosons in the limit of strong coupling. We construct algebraically exact duality and flux attachment transformations of the lattice theories, corresponding to analogous transformations in the continuum limit. These transformations are used to convert the model with arbitrary fractional Chern-Simons coefficient alpha to a model with alpha either zero or 1. We show that, unless the corrections of cubic and higher power in momenta, irrelevant near corresponding fixed points, render the phase transition first order, the phase transition in the original model is either in the 3D x-y or a ''fermionic'' universality class.