Instanton Solutions from Abelian Sinh-Gordon and Tzitzeica Vortices

Contatto, F.; Dorigoni, D.

Abstract

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 Poincaré 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 Kähler manifold with non-vanishing scalar curvature. The instantons we construct in this way cannot be obtained via a twistorial approach.

Citation

Contatto, F., & Dorigoni, D. (2015). Instanton Solutions from Abelian Sinh-Gordon and Tzitzeica Vortices. Journal of Geometry and Physics, 98, 429-445. https://doi.org/10.1016/j.geomphys.2015.08.021

• Journal Article Type: Article
• Acceptance Date: Aug 28, 2015
• Online Publication Date: Sep 5, 2015
• Publication Date: 2015-12
• Deposit Date: Dec 30, 2015
• Publicly Available Date: Sep 5, 2016
• Journal: Journal of Geometry and Physics
• Print ISSN: 0393-0440
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 98
• Pages: 429-445
• DOI: https://doi.org/10.1016/j.geomphys.2015.08.021
• Related Public URLs: http://arxiv.org/abs/1412.8312