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

Abstract

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 $\mathbb{R}\times G/H$. 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 $\mathbb{R}\times S^3$ 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.

16 pages, LaTeX 2e

References in corpus (6)

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• Smooth static solutions of the Einstein-Yang/Mills equation
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Cited by in corpus (3)

• Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
• Transition Probability (Fidelity) and Its Relatives
• Connections and Metrics Respecting Standard Purification