nLab Seiberg-Witten theory



Quantum field theory




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.



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

The original articles:


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

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

In relation to integrable systems:

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

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

  • 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]

See also:

Seiberg-Witten curve

SW-curve in SW-theory

The notion of the Seiberg-Witten curve in Seiberg-Witten theory originates in:


and in relation to integrable systems:

As M5-brane worldvolume

Observation that under geometric engineering of D=4 N=2 SYM on D4/NS5 intersections and further lift to a single M5-brane, the SW-curve is identified with the M5-worldvolume transverse to the SYM-spacetime:

Further early discussion:

Review in:

Quantum SW-curve

On the “quantum SW curve”, a kind of quantized SW curve:

In relation to class S-theories and “M3-brane”-defect branes inside M5-branes:

In relation to E-strings and D6-D8-brane bound states:

On why the SW-curve should be quantized this way, as seen from topological string theory:

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]

Last revised on July 8, 2024 at 06:29:54. See the history of this page for a list of all contributions to it.