Vortex solutions of the Liouville equation

Abstract

The most general vortex solution of the Liouville equation (which arises in non-relativistic Chern-Simons theory) is associated with rational functions, $f(z)=P(z)/Q(z)$ where $P(z)$ and $Q(z)$ are both polynomials, $°P<°Q\equiv N$. This allows us to prove that the solution depends on $4N$ parameters without the use of an index theorem, as well as the flux quantization~: $\Phi =-4N\pi (sign\kappa )$.

11 pages, Plain Tex, no figures