Science China Mathematics

, Volume 60, Issue 6, pp 1089–1100 | Cite as

Seiberg-Witten theory as a complex version of Abelian Higgs model

Articles

Abstract

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.

Keywords

Ginzburg-Landau equations vortices Seiberg-Witten equations 

MSC(2010)

53D42 53Z05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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