Liouville Vortex And $\varphi^{4}$ Kink Solutions Of The Seiberg--Witten Equations

Details Liouville Vortex And $\varphi^{4}$ Kink Solutions Of The Seiberg--Witten Equations Liouville Vortex And $\varphi^{4}$ Kink Solutions Of The Seiberg--Witten Equations

1996-02-16

arxiv.org/abs/hep-th/9602088v1

J.Math.Phys. 37 (1996) 3753-3759

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Latex

Scientific paper

10.1063/1.531628

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

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