Geodesic
Seiberg--Witten Equations and Complex Abrikosov Strings
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 224-261

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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. 
@article{TM_2001_235_a15,
     author = {A. G. Sergeev},
     title = {Seiberg--Witten {Equations} and {Complex} {Abrikosov} {Strings}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {224--261},
     publisher = {mathdoc},
     volume = {235},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_235_a15/}
}
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A. G. Sergeev. Seiberg--Witten Equations and Complex Abrikosov Strings. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 224-261. http://geodesic.mathdoc.fr/item/TM_2001_235_a15/