Modification of Einstein-Yang-Mills theory from dimensional reduction of the Gauss-Bonnet action

Dimensional reduction of a sum of the Einstein-Hilbert and Gauss-Bonnet action in n dimensions leads to a modified four-dimensional Einstein-Yang-Mills action. The latter contains a special non-minimal coupling between curvature and Yang-Mills field strength which contributes at most second derivatives of the four-dimensional metric and the Yang-Mills potential to the field equations.