Seiberg-Witten theory as a complex version of Abelian Higgs model
The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2 + 1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg-Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex (2+2)-dimensional version of the (2 + 1)-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in (2+1)-dimensional case.
KeywordsGinzburg-Landau equations vortices Seiberg-Witten equations
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This work was supported by Russian Foundation of Basic Research (Grants Nos. 16-01-00117 and 16-52-12012), the Program of support of Leading Scientific Schools (Grants No. NSh-9110.2016.1) and the Program of Presidium of Russian Academy of Sciences “Nonlinear dynamics”.