Selfgravitating Yang-Mills solitons and their Chern-Simons numbers

Details Selfgravitating Yang-Mills solitons and their Chern-Simons numbers Selfgravitating Yang-Mills solitons and their Chern-Simons numbers

1993-08-26

arxiv.org/abs/gr-qc/9308028v1

J.Math.Phys.35:899-919,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, Latex, report ZU-TH 23/93, figure can be obtained from the authors

Scientific paper

10.1063/1.530620

We present a classification of the possible regular, spherically symmetric solutions of the Einstein-Yang-Mills system which is based on a bundle theoretical analysis for arbitrary gauge groups. It is shown that such solitons must be of magnetic type, at least if the magnetic Yang-Mills charge vanishes. Explicit expressions for the Chern-Simons numbers of these selfgravitating Yang-Mills solitons are derived, which involve only properties of irreducible root systems and some information about the asymptotics of the solutions. It turns out, as an example, that the Chern-Simons numbers are always half-integers or integers for the gauge groups $SU(n)$. Possible physical implications of these results, which are based on analogies with the unstable sphaleron solution of the electroweak theory, are briefly indicated.

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