Lines vortices in the \(U(1)\)-Higgs model. (English) Zbl 0874.53019

From the paper: “For a given U(1)-bundle \(E\) over \(M=\mathbb{R}^3\setminus \{x_1,\dots,x_n\}\), where the \(x_i\) are \(n\) distinct points of \(\mathbb{R}^3\), we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitly and which is singular along line vortices which connect the \(x_i\)”.


53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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