Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices

JOURNAL OF GEOMETRY AND PHYSICS

卷:98

Article

Contatto, Felipe^1,2  Dorigoni, Daniele¹ 

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

[2] Minist Educ Brazil, CAPES Fdn, BR-70040020 Brasilia, DF, Brazil

关键词: Vortices;    Ginzburg-Landau;    Conical singularity;    Orbifold;    Instantons;   

DOI  :  10.1016/j.geomphys.2015.08.021

来源: Elsevier

【 摘 要 】

We study the Abelian Higgs vortex solutions to the sinh-Gordon equation and the elliptic Tzitzeica equation. Starting from these particular vortices, we construct solutions to the Taubes equation with higher vortex number, on surfaces with conical singularities. We then, analyse more general properties of vortices on such singular surfaces and propose a method to obtain vortices on conifolds from vortices on surfaces of revolution. We apply our method to construct explicit vortex solutions on the Poincare disk with a conical singularity in the centre, to which we refer as the hyperbolic cone. We uplift the Abelian sinh-Gordon and Tzitzeica vortex solutions to four dimensions and construct cylindrically symmetric, self-dual Yang-Mills instantons on a non-self-dual (nor anti-self-dual) 4-dimensional Kahler manifold with non-vanishing scalar curvature. The instantons we construct in this way cannot be obtained via a twistorial approach. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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