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.

 

 

4-manifolds

• 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

application to 4-manifolds

• invariants of compact smooth 4-manifolds introduced by Witten (1994)

related items

• N=2 supersymmetric theory in d=4
• theory of 4-manifold 

encyclopedia

• http://en.wikipedia.org/wiki/Seiberg%E2%80%93Witten_gauge_theory
• http://en.wikipedia.org/wiki/Seiberg%E2%80%93Witten_invariant

expositions

• Bohn, Michael. 2007. “An introduction to Seiberg-Witten theory on closed 3-manifolds”. 0706.3604 (6월 25). http://arxiv.org/abs/0706.3604
• Nastase
  • Susy, sugra, strings, branes, duality
  • Duality
  • Supersymmetry in 4d
  • Seiberg-Witten theory
• 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.

video lectues

• Witten
  • Seiberg-Witten Theory, Part 1
  • Seiberg-Witten Theory, Part 2

articles

• 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.