Abstract
We investigate all possible solutions of the six-dimensional Einstein-Yang-Mills equations with four-dimensional Poincaré invariance and geometry M 4 × B. (B is a two-dimensional internal space with finite volume.) Excluding the trivial case of B being flat, we find that for all solutions the internal space is a sphere and the gauge fields are in a monopole configuration on S 2. Therefore, the isometry group SO(3) is not spontaneously broken.
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