Vortex Solutions of the Liouville Equation

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The most general vortex solution of the Liouville equation (which arises in nonrelativistic 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 ≡ 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 Φ=-Nπ(sign k).

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