The Bogomolny Equations and Solutions for Einstein-Yang-Mills-Dilaton- $σ$ Models
Abstract
Description
We derive Bogomolny equations for an Einstein-Yang-Mills-dilaton-$σ$ model (EYMD-$σ$) 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).
24 pages LaTex, 1 Figure, revised text for publication
24 pages LaTex, 1 Figure, revised text for publication