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arXiv · 2406.20043

On the Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane

William L. Blair·Minh Lam Nguyen
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Abstract

Clifford Taubes showed that the moduli space of the variational equations of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to "vortices". Inspired by this result, in this paper, we completely characterize exponential decay solutions to the Seiberg-Witten vortex equations, where the equations are derived by applying a Hitchin-type dimensional reduction. We show that the existence of Seiberg-Witten ``vortices'' is not provided by the exponential decay solutions. This is in contrast to the Yang-Mill-Higgs vortex equations.

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William L. Blair, Minh Lam Nguyen. 2024-06-28. On the Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane. https://arxiv.org/abs/2406.20043

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