Topologically induced instability in string theory

Abstract

Using Witten's generalised AdS/CFT correspondence, we show that there are certain differentiate manifolds Z10 such that string theory is unstable (to the emission of "large branes") on Z10 no matter what the metric may be. Therefore, the instability is due to the (differential) topology of the background, not to its geometry. We propose a precise formulation of this restriction on the topology of string backgrounds, and give evidence for its validity. The discussion is designed to introduce particular geometric/topological techniques which are likely to be useful in further applications of the AdS/CFT correspondence.