On quasi-normal modes and the AdS_5/CFT_4 correspondence

Details On quasi-normal modes and the AdS_5/CFT_4 correspondence On quasi-normal modes and the AdS_5/CFT_4 correspondence

2004-07-18

arxiv.org/abs/hep-th/0407157v2

Nucl.Phys. B715 (2005) 483-498

Physics

High Energy Physics

High Energy Physics - Theory

v2: 20 pages, added discussion on geometric origin of results, corrected typos; to appear in Nucl. Phys. B

Scientific paper

10.1016/j.nuclphysb.2005.03.023

We discuss the quasi-normal modes of massive scalar perturbations of black holes in AdS_5 in conjunction with the AdS/CFT correspondence. On the gravity side, we solve the wave equation and obtain an expression for the asymptotic form of quasi-normal frequencies. We then show that these expressions agree with those obtained from a CFT defined on $\mathbb{R} \times S^3$ in a certain scaling limit, by identifying Euclidean time with one of the periodic coordinates. This generalizes known exact results in three dimensions (BTZ black hole). As a by-product, we derive the standard energy quantization condition in AdS by a simple monodromy argument in complexified AdS space. This argument relies on an unphysical singularity.

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