Gauge Theory: Instantons, Monopoles, and Moduli Spaces

Details Gauge Theory: Instantons, Monopoles, and Moduli Spaces Gauge Theory: Instantons, Monopoles, and Moduli Spaces

2003-04-16

arxiv.org/abs/math-ph/0304026v1

Physics

Mathematical Physics

16 pages, no figures

Scientific paper

In this expository review we discuss various aspects of gauge theory. While the focus is on mathematics, wherever possible we make contact with theoretical high energy physics. Particular emphasis is placed on instantons and monopoles, which admit physical interpretation, and yield interesting and nontrivial mathematics. We give a clear and essentially self-contained exposition of the mathematical structure of the Seiberg-Witten monopole equations. Other topics include Donaldson's theorem on moduli spaces of monopoles, compactification of spaces of ASD connections, The Abelian monopole equations, and Abelian Higgs vortices.

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