Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$

Da Rong Cheng

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arXiv · 2007.10968

Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$

Da Rong Cheng

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Abstract

We show under natural assumptions that stable solutions to the abelian Yang--Mills--Higgs equations on Hermitian line bundles over the round $2$-sphere actually satisfy the vortex equations, which are a first-order reduction of the (second-order) abelian Yang--Mills--Higgs equations. We also obtain a similar result for stable solutions on a flat $2$-torus. Our method of proof comes from the work of Bourguignon--Lawson concerning stable $SU(2)$ Yang--Mills connections on compact homogeneous $4$-manifolds.

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Da Rong Cheng. 2020-07-21. Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$. https://arxiv.org/abs/2007.10968

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