Seiberg–Witten Equations and Complex Abrikosov Strings

An interpretation of Abrikosov strings in the Abelian $(2+1)$-dimensional Higgs model is given in terms of the adiabatic limit. In an analogous way, complex Abrikosov strings are interpreted in terms of the reduction of 4-dimensional Seiberg–Witten equations to pseudoholomorphic curves.