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arXiv · 1510.03810

Gravitating vortices, cosmic strings, and the Kähler--Yang--Mills equations

Luis Álvarez-Cónsul·Mario Garcia-Fernandez·Oscar García-Prada
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Abstract

In this paper we construct new solutions of the Kahler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, that we call gravitating vortex equations, describe Abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Szekelyhidi.

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Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada. 2016-06-24. Gravitating vortices, cosmic strings, and the Kähler--Yang--Mills equations. https://arxiv.org/abs/1510.03810

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