Seiberg–Witten theory

Summary

Seiberg–Witten theory is the exact description of the low-energy physics of four-dimensional $N = 2$ supersymmetric Yang–Mills theory, found by Nathan Seiberg and Edward Witten in 1994. The vacua of the theory form a complex curve, the Coulomb branch. Over each vacuum sits an elliptic curve whose periods give the low-energy coupling constant. At special vacua, magnetic monopoles become massless, and a dual description in terms of these monopoles takes over. This picture led Witten to the Seiberg–Witten invariants of four-manifolds, and later to links with integrable systems and enumerative geometry.