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Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices.

Contatto, F. and Dorigoni, D. (2015) 'Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices.', Journal of geometry and physics., 98 . pp. 429-445.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.geomphys.2015.08.021
Publisher statement:© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:28 August 2015
Date deposited:29 March 2016
Date of first online publication:05 September 2015
Date first made open access:05 September 2016

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