Critical properties of the topological Ginzburg-Landau model

We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons term added. The flow diagram contains two charged fixed points corresponding to the tricritical and infrared stable fixed points. The topological coupling controls the fixed-point structure and eventually the region of first-order transitions disappears. We compute the critical exponents as a function of the topological coupling. We obtain that the value of the ν exponent does not vary very much from the XY value, ν_XY=0.67. This shows that the Chern-Simons term does not affect considerably the XY scaling of superconductors. We discuss briefly the possible phenomenological applications of this model.