This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an em...This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.展开更多
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 equa...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＋l）-dimensional case.展开更多
We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show ...We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.展开更多
In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuch...In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres–Douglas points. Furthermore, we obtain the solution of these differential equations.展开更多
文摘This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.
基金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)the Program of Presidium of Russian Academy of Sciences“Nonlinear dynamics”
文摘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＋l）-dimensional case.
文摘We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.
文摘In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres–Douglas points. Furthermore, we obtain the solution of these differential equations.
