A certain class of Einstein-Yang-Mills systems

A class of G-invariant Einstein-Yang-Mills (EYM) systems with cosmological constant on homogeneous spaces GH, where G is a semisimple compact Lie group, is presented. These EYM systems can be obtained in terms of dimensional reduction of pure gravity. If GH is a symmetric space, the EYM system on GH provides a static solution of the EYM equations on space-time R × GH. This way, in particular, a solution for an arbitrary Lie group F, considered as a symmetric space, is obtained. This solution is discussed in detail for the case F = SU(2). A known analytical EYM system on R × S3 is recovered and it is shown—using a relation to the BPST instanton—that this solution is of sphaleron type. Finally, a relation to the distance of Bures and to parallel transport along mixed states is shown.