Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-07-30
Int.J.Mod.Phys. A17 (2002) 4463-4514
Physics
High Energy Physics
High Energy Physics - Theory
51 pages, 10 figures, 8 postscript files. Submitted to International Journal of Modern Physics A, July 2002 Uses Latex 2e with
Scientific paper
10.1142/S0217751X0201217X
In 1983, Donaldson shocked the topology world by using instantons from physics to prove new theorems about four-dimensional manifolds, and he developed new topological invariants. In 1988, Witten showed how these invariants could be obtained by correlation functions for a twisted N=2 SUSY gauge theory. In 1994, Seiberg and Witten discovered dualities for such theories, and in particular, developed a new way of looking at four-dimensional manifolds that turns out to be easier, and is conjectured to be equivalent to, Donaldson theory. This review describes the development of this mathematical subject, and shows how the physics played a pivotal role in the current understanding of this area of topology.
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