Abstract
We discuss black hole and black string solutions in d=5 Einstein–Yang–Mills theory with negative cosmological constant, proposing a method to compute their mass and action. The magnetic gauge field of these configurations does not vanish at infinity. We argue that this implies a nonvanishing trace for the stress tensor of the dual d=4 theory.
Highlights
Introduction.– As originally found in d = 4 spacetime dimensions [1], [2], a variety of well known features of asymptotically flat self-gravitating non-Abelian solutions are not shared by their anti-de Sitter (AdS) counterparts
The coefficient of the divergent term in the action is related in this case to the trace anomaly of the dual CFT defined in a background non-Abelian magnetic field
As r → ∞, the spacetime is locally isometric to AdS spacetime, and we find the following asymptotic expression of the solutions
Summary
In contrast with the four dimensional case, a generic property of d > 4 non-Abelian solutions is that their mass and action, as defined in the usual way, diverge [4, 5], which may raise questions about their physical relevance. The coefficient of the divergent term in the action is related in this case to the trace anomaly of the dual CFT defined in a background non-Abelian magnetic field. Non-Abelian black hole solutions.– The action of the d = 5 gauged supergravities usually contain the YM term LY M = −1/(2e2)Tr{FμνF μν} as a basic building block (with Fμν the field strength and e the gauge coupling constant).
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