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

Abstract

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 ${\phi }^4$ theory.

14 pages, Latex

References in corpus (3)

• Supersymmetric Yang-Mills Theory On A Four-Manifold
• Lectures on Seiberg-Witten Invariants
• Dirac Monopoles and Witten's Monopole Equations

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