The Bogomolny Equations and Solutions for Einstein-Yang-Mills-Dilaton- $σ$ Models

H. W. Braden, V. Varela

Published 1998-04-30, updated 1998-09-11Version 2

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).