Vortex solutions of the Liouville equation

Details Vortex solutions of the Liouville equation Vortex solutions of the Liouville equation

1998-05-25

arxiv.org/abs/hep-th/9805161v1

Lett.Math.Phys. 46 (1998) 111-120

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Plain Tex, no figures

Scientific paper

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, $\deg P<\deg Q\equiv N$. 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~: $\Phi=-4N\pi(sign \kappa)$.

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