SU(3) Einstein-Yang-Mills-Dilaton Sphalerons and Black Holes

SU(3) Einstein-Yang-Mills-dilaton theory possesses sequences of static spherically symmetric sphaleron and black hole solutions for the SU(2) and the SO(3) embedding. The solutions depend on the dilaton coupling constant $\gamma$, approaching the corresponding Einstein-Yang-Mills solutions for $\gamma \rightarrow 0$, and Yang-Mills-dilaton solutions in flat space for $\gamma \rightarrow \infty$. The sequences of solutions tend to Einstein-Maxwell-dilaton solutions with different magnetic charges. The solutions satisfy analogous relations between the dilaton field and the metric for general $\gamma$. Thermodynamic properties of the black hole solutions are discussed.