Liouville vortex and φ4 kink solutions of the Seiberg–Witten equations

The Seiberg--Witten equations, when dimensionally reduced to $\bf R^{2}\mit$,naturally yield the Liouville equation, whose solutions are parametrized by anarbitrary analytic function $g(z)$. The magnetic flux $\Phi$ is the integral ofa singular Kaehler form involving $g(z)$; for an appropriate choice of $g(z)$ ,$N$ coaxial or separated vortex configurations with $\Phi=\frac{2\pi N}{e}$ areobtained when the integral is regularized. The regularized connection in the$\bf R^{1}\mit$ case coincides with the kink solution of $\varphi^{4}$ theory.Comment: 14 pages, Late