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

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