# The Bogomolny Equations and Solutions for Einstein-Yang-Mills-Dilaton- $\sigma$ Models

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Published Article
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DOI: 10.1103/PhysRevD.58.124020
arXiv ID: hep-th/9804204
Source
arXiv
We derive Bogomolny equations for an Einstein-Yang-Mills-dilaton-$\sigma$ model (EYMD-$\sigma$) on a static spacetime, showing that the Einstein equations are satisfied if and only if the associated (conformally scaled) three-metric is flat. These are precisely the static metrics for which super-covariantly constant spinors exist. We study some general properties of these equations and then consider the problem of obtaining axially symmetric solutions for the gauge group SU(2).