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In any non-Abelian gauge theory, any maximum Abelian gauge is an incomplete gauge which fixes the gauge freedom outside of the maximum Abelian subgroup.
Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.
2010 Gerald Guralnik, C. R. Hagen, Tom Kibble, Robert Brout, Francois Englert, and Peter Higgs: "For elucidation of the properties of spontaneous symmetry breaking in four-dimensional relativistic gauge theory and of the mechanism for the consistent generation of vector boson masses." See also 1964 PRL symmetry breaking papers, Higgs mechanism, and Higgs boson.
BPS vortices, which are those vortices that preserve some supersymmetry, have masses which are given by the FI term of the gauge theory.
Spin Networks in Gauge Theory, John C. Baez, Advances in Mathematics, Volume 117, Number 2, February 1996, pp.