Einstein-Yang-Mills theory in 4 + d dimensions admits a solution of the form M4 × G/H, where M4 is Einstein and G/H is symmetric, if the gauge group is H (or larger). The gauge fields of this solution are topologically nontrivial. The symmetry group is G4 × G × H, G4 being the isometry group of M4; M4 could be Minkowski or anti-de Sitter space.
