A proposal for studying off-shell stability of vacuum geometries in string theory

We briefly review studies of off-shell stability of vacuum geometries in semiclassical gravity. We propose a study of off-shell stability of vacua in string theory by a distinct, though somewhat related approach, by studying their stability under suitable world-sheet sigma model renormalization group (RG) flows. Stability under RG flow is a mathematically well-posed and tractable problem in many cases, as we illustrate through examples. The advantage is that we can make definite predictions about late time behaviour and endpoints of off-shell processes in string theory.