Colorful Horizons with Charge in Anti-de Sitter Space

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstrom-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a diagonal combination of gauge invariance and spatial rotational invariance.