Seiberg-Witten理论作为阿贝尔Higgs模型的复杂版本
Seiberg-Witten theory as a complex version of Abelian Higgs model
摘要：
绝热极限方法将（2 + 1）维阿贝尔Higgs模型的每一个解与静态解的模空间中的测地线联系起来。我们表明，同样的程序Seiberg-Witten方程的4维辛流形介绍Taubes可以被认为是一个复杂的（2 + 2）维版本的（2 + 1）维图片。更确切地说，在4维情况下的绝热极限程序与Seiberg-Witten方程的解相关联，该方程是一个伪全纯因子，在（2 + 1）维情况下，该因子可以被视为测地线的复形式。
英文摘要：
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 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.
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