A certain class of Einstein-Yang-Mills--systems

Details A certain class of Einstein-Yang-Mills--systems A certain class of Einstein-Yang-Mills--systems

1996-03-12

arxiv.org/abs/gr-qc/9603017v1

Rept.Math.Phys. 39 (1997) 433-446

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, LaTeX 2e

Scientific paper

10.1016/S0034-4877(97)89758-3

A class of $ G $-invariant Einstein-Yang-Mills (EYM) systems with cosmological constant on homogeneous spaces $ G / H $, 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 $ G / H $ is a symmetric space, the EYM--system on $ G / H $ provides a static solution of the EYM--equations on spacetime $ {\Bbb R} \times G / H $. 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 $ {\Bbb R} \times S^3 $ 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.

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