Seiberg-Witten theory as a complex version of Abelian Higgs model
arXiv:1702.04882 · doi:10.1007/s11425-016-9030-4
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.
This paper of 13 pages is dedicated to the memory of Professor Lu Qikeng. Accepted for publication in 2017