Abstract
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.
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Acknowledgments
Part of this work was carried out when the author was visiting Beijing International Center for Mathematical Research. The author would like to thank Prof. Gang Tian for his constant support. He would also like to thank Prof. Youde Wang, Yuxiang Li, Miaomiao Zhu and Li Chen for many helpful discussions. Supported by NSFC No. 11201387, SRFDP grant No. 20120121120022 and the Natural Science Foundation of Fujian Province of China (No. 2014J01023).
