We consider solutions of the four-dimensional Einstein-Yang-Mills (EYM) system with a negative cosmological constant $\Lambda =-3g^2$, where $g$ is the non-Abelian gauge coupling constant. This theory corresponds to a consistent truncation of $\mathcal{N}=4$ gauged supergravity and may be uplifted to $d=11$ supergravity. A systematic study of all known solutions is presented as well as new configurations corresponding to rotating regular dyons and rotating non-Abelian black holes. The thermodynamics of the static black hole solutions is also discussed. The generic EYM solutions present a nonvanishing magnetic flux at infinity and should give us information about the structure of a conformal field theory (CFT) in a background SU(2) field. We argue that the existence of these configurations violating the no-hair conjecture is puzzling from the anti-de Sitter (AdS)/CFT point of view.

• Received 7 June 2006

DOI:https://doi.org/10.1103/PhysRevD.74.064015