Stable solutions to the abelian Yang--Mills--Higgs equations on S²\n and T²

2020/07/21 by Da Rong Cheng, Cheng, Da Rong
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2007.10968

openalex publication_date 2020/07/21 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We show under natural assumptions that stable solutions to the abelian\nYang--Mills--Higgs equations on Hermitian line bundles over the round\n2-sphere actually satisfy the vortex equations, which are a first-order\nreduction of the (second-order) abelian Yang--Mills--Higgs equations. We also\nobtain a similar result for stable solutions on a flat 2-torus. Our method of\nproof comes from the work of Bourguignon--Lawson concerning stable SU(2)\nYang--Mills connections on compact homogeneous 4-manifolds.\n

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