Yang-Mills solitons in models with conformal symmetry breaking

Finite energy particle-like solutions of conformally invariant theories in flat space are ruled out by Coleman, Deser and Pagels arguments, so there are no purely Yang-Mills solitons for usual YM action in flat space. Meanwhile, such solitons do exist, if the YM fields are governed by the non-Abelian Born-Infeld effective action arising in string theory. These are similar to Bartnik McKinnon particle-like solutions in Einstein-Yang-Mills theory. Both theories break conformal symmetry of the classical action thus avoiding the above no-go result. Topologically they are similar to sphalerons of the electroweak theory, where breaking of conformal symmetry is due to the Higgs field. We review these and others solutions including Einstein-Yang-Mills vortices, and discuss some other effects of breaking of conformal symmetry on classical YM fields: stabilization of chaos and cosmological inflation.