Nonabelian solutions in AdS_4 and d=11 supergravity

Abstract

We consider solutions of the four dimensional Einstein-Yang-Mills system with a negative cosmological constant $\Lambda =-3g^2$, where $g$ is the nonabelian 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 nonabelian 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 CFT in a background SU(2) field. We argue that the existence of these configurations violating the no hair conjecture is puzzling from the AdS/CFT point of view.

52 pages; 24 figures; v2: minor changes, references added, version to be published in PRD

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• Dyonic black holes in $\mathfrak{su}(\infty )$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinite set of global charges