Nonabelian solutions in AdS_4 and d=11 supergravity

TL;DR

This paper explores nonabelian solutions in four-dimensional Einstein-Yang-Mills theory with negative cosmological constant, including new rotating black holes and dyons, and discusses their implications for AdS/CFT correspondence.

Contribution

It systematically studies known and new nonabelian solutions in AdS_4, including rotating configurations, and analyzes their thermodynamics and holographic implications.

Findings

Discovery of rotating nonabelian black holes and dyons.

Analysis of thermodynamics of static black hole solutions.

Insights into CFT structure with background SU(2) fields.

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 ${\cal N}=4$ 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.