Anyonic superconductivity

The renormalized Chern-Simons term at finite density is shown to vanish when the renormalized coefficient at zero density takes values $\frac{{\mathrm{Ne}}^2}{2\pi }$. Thus in the Chern-Simons description a system of anyons at zero temperature is a superfluid. This result is shown to hold to all orders in perturbation theory by generalizing a nonrenormalization theorem of the zero-density case. We also discuss the finite-temperature case, where a perturbative Chern-Simons mass appears.