Convergence of Yang-Mills-Higgs fields
Abstract
In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann 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) after finitely many times of blowing-up's. In particular, we prove a generalized energy identity and give a refined analysis of the neck.
Keywords
Cite
@article{arxiv.1403.0780,
title = {Convergence of Yang-Mills-Higgs fields},
author = {Chong Song},
journal= {arXiv preprint arXiv:1403.0780},
year = {2014}
}
Comments
45 pages. The degenerate case is investigated in the new version. Comments welcome