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Instanton Solutions from Abelian Sinh-Gordon and Tzitzeica Vortices

Contatto, F.; Dorigoni, D.

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Authors

F. Contatto



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

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