Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations

Takashi Ono

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arXiv · 2509.07489

Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations

Takashi Ono

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Abstract

Let $X$ be a compact Riemann surface and $\mathbb{P}^1$ be the complex projective line. In this paper, we introduce an equation which we call the doubly-coupled vortex equation on $X$. We show that the existence of a solution of the doubly-coupled is equivalent to the existence of an $SU(2)$-invariant Hermitian-Einstein metric on certain Higgs bundles over $X\times \mathbb{P}^1$. By applying the Kobayashi-Hitchin correspondence for Higgs bundles, we further show that the existence of a solution to the doubly-coupled vortex equation is equivalent to the stability of the associated Higgs quadruplet.

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Takashi Ono. 2025-09-09. Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations. https://arxiv.org/abs/2509.07489

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