Seiberg-Witten theory

introduction

Vortices and Monopoles and Instantons
After describing the gauge theory of Electromagnetism, we shall define the 4-dimensional Seiberg-Witten invariant (sweeping much technical structure under the rug) and discuss its topological properties.
Then we'll backtrack and try to see how this physics beast was born.

1980's work of M. Freedman gave a new insight in the topological classification of simply connected compact 4-manifolds via their intersection forms
Donaldson succeeded in establishing criteria how the intersection form can prevent a topological 4-manifold from being smoothable

Bohn, Michael. 2007. “An introduction to Seiberg-Witten theory on closed 3-manifolds”. 0706.3604 (6월 25). http://arxiv.org/abs/0706.3604
Nastase
Lerche, W. 1997. “Introduction to Seiberg-Witten Theory and Its Stringy Origin.” Fortschritte Der Physik. Progress of Physics 45 (3-4): 293–340. doi:10.1002/prop.2190450304.

Furuta, Mikio, and Shinichiroh Matsuo. “The Perturbation of the Seiberg-Witten Equations Revisited.” arXiv:1405.1219 [math], May 6, 2014. http://arxiv.org/abs/1405.1219.
Seiberg, Nathan, and Edward Witten. “Gauge Dynamics And Compactification To Three Dimensions.” arXiv:hep-th/9607163, July 18, 1996. http://arxiv.org/abs/hep-th/9607163.
Seiberg, N., and E. Witten. “Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory.” Nuclear Physics B 426, no. 1 (September 1994): 19–52. doi:10.1016/0550-3213(94)90124-4.
Seiberg, N., and E. Witten. “Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD.” Nuclear Physics B 431, no. 3 (December 1994): 484–550. doi:10.1016/0550-3213(94)90214-3.