Stability in Asymptotically AdS Spaces

TL;DR

This paper investigates both perturbative and non-perturbative instabilities in string theory compactifications to asymptotically AdS spaces, providing classifications and examples, with implications for stability in AdS/CFT contexts.

Contribution

It offers a complete characterization of instabilities in three-dimensional Einstein manifolds and partial classification in higher dimensions, extending the Breitenlohner-Freedman bound.

Findings

Most Euclidean asymptotically AdS spaces with multiple boundaries are unstable under certain conditions.

Examples include quotients of AdS and AdS Taub-NUT spaces, which can be unstable perturbatively and non-perturbatively.

A previously discussed space in AdS/CFT is shown to be unstable in both senses.

Abstract

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.