Stability in Asymptotically AdS Spaces

Details Stability in Asymptotically AdS Spaces Stability in Asymptotically AdS Spaces

2004-09-23

arxiv.org/abs/hep-th/0409242v1

JHEP0508:016,2005

Physics

High Energy Physics

High Energy Physics - Theory

18 pages and 5 figures

Scientific paper

10.1088/1126-6708/2005/08/016

We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the case of three dimensional Einstein manifolds, we completely characterize the presence of these instabilities, and in higher dimensions we provide a partial classification. The analysis may be viewed as an extension of the Breitenlohner-Freedman bound. One interesting result is that, apart from a very special class of exceptions, all Euclidean asymptotically AdS spaces with more than one conformal boundary component are unstable, if the compactification admits BPS branes or scalars saturating the Breitenlohner-Freedman bound. As examples, we analyze quotients of AdS in any dimension and AdS Taub-NUT spaces, and show a space which was previously discussed in the context of AdS/CFT is unstable both perturbatively and non-perturbatively.

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