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arXiv · 2206.03327

The Yang-Mills-Higgs functional on complex line bundles: $Γ$-convergence and the London equation

Giacomo Canevari·Federico Luigi Dipasquale·Giandomenico Orlandi
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Abstract

We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension $n\geq 3$. This functional is the natural generalisation of the Ginzburg-Landau model for superconductivity to the non-Euclidean setting. We prove a $Γ$-convergence result, in the strongly repulsive limit, on the functional rescaled by the logarithm of the coupling parameter. As a corollary, we prove that the energy of minimisers concentrates on an area-minimising surface of dimension $n-2$, while the curvature of minimisers converges to a solution of the London equation.

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Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi. 2023-05-22. The Yang-Mills-Higgs functional on complex line bundles: $Γ$-convergence and the London equation. https://arxiv.org/abs/2206.03327

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