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We derive Bogomolny equations for an Einstein-Yang-Mills-dilaton-$\sigma$model (EYMD-$\sigma$) on a static spacetime, showing that the Einsteinequations are satisfied if and only if the associated (conformally scaled)three-metric is flat. These are precisely the static metrics for whichsuper-covariantly constant spinors exist. We study some general properties ofthese equations and then consider the problem of obtaining axially symmetricsolutions for the gauge group SU(2).Comment: 24 pages LaTex, 1 Figure, revised text for publicatio

Bogomol’nyi equations and solutions for Einstein-Yang-Mills-dilaton-σ models