nLab Seiberg-Witten theory

Idea

Seiberg-Witten theory studies the moduli space of vacua in N=2 D=4 super Yang-Mills theory, in particular the electric-magnetic duality (Montonen-Olive duality) of the theory.

Related concepts

• N=2 D=4 super Yang-Mills theory

• Coulomb branch, Higgs branch

• Donaldson theory

• Chern-Simons theory, topological Yang-Mills theory

• topologically twisted D=4 super Yang-Mills theory

• AGT correspondence

References

General

For more and for general references see at N=2 D=4 super Yang-Mills theory.

The original articles are

• Nathan Seiberg, Edward Witten, Monopole condensation, and confinement in $N=2$ supersymmetric Yang-Mills theory, Nucl.Phys. B426:19–52, 1994; Erratum-ibid. B430:485–486, 1994 (arXiv:hep-th/9407087)
• Nathan Seiberg, Edward Witten, Monopoles, duality and chiral symmetry breaking in $N=2$

  supersymmetric QCD, Nucl. Phys. B431 (1994) 484–550, hep-th/9408099

Reviews include

• Jürgen Einhorn, Thomas Friedrich, Seiberg-Witten theory (pdf)

• Simon Donaldson, The Seiberg-Witten equations and 4-manifold topology (pdf)

• Matilde Marcolli, Seiberg-Witten gauge theory, pdf

• piljin yi, Seiberg-Witten theory – with a view toward MQCD (pdf)

• Wikipedia, Seiberg-Witten invariants

A useful discussion of the physical origins of the Seiberg-Witten equations for mathematicians is in

• Siye Wu, The Geometry and Physics of the Seiberg-Witten Equations, Progress in mathematics, volume 205 (2002)

Discussion of lifts of SW-invariants to M-theory includes

• Neil Lambert, Peter West, Monopole Dynamics from the M-Fivebrane, Nucl.Phys. B556 (1999) 177-196 (arXiv:hep-th/9811025)

A lift of Seiberg-Witten invariants to classes in circle group-equivariant stable cohomotopy is discussed in

• M. Furuta, (2001), Monopole Equation and the 11/8-Conjecture , Mathematical Research Letters 8: 279–291 (doi)

• Stefan Bauer, Mikio Furuta, A stable cohomotopy refinement of Seiberg-Witten invariants: I (arXiv:math/0204340)

• Stefan Bauer, A stable cohomotopy refinement of Seiberg-Witten invariants: II (arXiv:math/0204267)

Relation to Rozansky-Witten invariants

On relation between Rozansky-Witten invariants and Seiberg-Witten invariants of 3-manifolds:

• Matthias Blau, George Thompson, On the Relationship between the Rozansky-Witten and the 3-Dimensional Seiberg-Witten Invariants, Adv. Theor. Math. Phys. 5 (2002) 483–498 (arXiv:hep-th/0006244)