  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. This is a contribution
to the proceedings of Theory Canada 4, CRM Montreal.
