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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（6）
• 页码范围: 1089-1100
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11425-016-9030-4

摘要

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 SeibergWitten 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.