Particle-like solutions to higher order curvature Einstein--Yang-Mills systems in d dimensions

We consider the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the superposition of the first two members of the $SO_{(\pm)}(d)$ Yang--Mills hierarchy, in $d$ dimensions. Such systems can occur in the low energy effective action of string theory. Particle-like solutions %for the systems with only an Einstein term, and with only a GB term, in dimensions $d=6,8$ are constructed respectively. Our results reveal qualitatively new properties featuring double-valued solutions with critical behaviour. In this preliminary study, we have restricted ourselves to one-node solutions.