Topology change in Kaluza-Klein and superstring theories

Abstract

It is shown that topology change-for instance, true dynamical compactification - cannot occur in classical Kaluza-Klein and superstring theories without causality violation either in the form of a breakdown in predictability (a failure of global hyperbolicity), or in the form of closed timelike curves. This implies that if causality holds, then any topological distinction between the spacetime and internal dimensions either has to be present ab initio, or else must arise in the quantum gravity regime.