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 $\nu$ exponent does not vary very much from the XY value, $\nu_{XY}=0.67$. 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.