Convergence of Yang–Mills–Higgs fields

In this paper, we study the convergence of Yang–Mills–Higgs (YMH) fields defined on fiber bundles over Riemann surfaces, where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary. We show that away from the nodes, the YMH fields converges, up to gauge, to a smooth YMH field modulo finitely many harmonic spheres, while near the nodes where the conformal structure degenerates, the YMH fields converges to a pair consisting of a flat connection and a twisted geodesic (with potential). In particular, we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general YMH fields.