The Fate of Unstable Gauge Flux Compactifications
  Fluxes are widely used to stabilise extra dimensions, but if they arise within a non-abelian gauge sector they are often unstable. We seek the fate of this instability, focussing on the simplest examples: sphere-monopole compactifications in six dimensions. Without gravity most non-abelian monopoles are unstable, decaying into the unique stable monopole in the same topological class. We show that the same is true in Einstein-YM systems, with the geometry adjusting accordingly: a Mink(d)xS2 geometry supported by an unstable monopole relaxes to an AdS(d)xS2. For 6D supergravity, the dilaton obstructs this simple evolution, acquiring a gradient and thus breaking some of the spacetime symmetries. We argue that it is the 4D symmetries that break, and examine several endpoint candidates. Oxidising the supergravity system into a higher-dimensional Einstein-YM monopole, we use the latter to guide us to the corresponding endpoint. The result is a singular Kasner-like geometry conformal to Mink(4)xS2. The solution has lower potential energy and is perturbatively stable, making it a sensible candidate endpoint for the evolution. (Abridged abstract for arXiv.) 
C.P. Burgess, S.L. Parameswaran, I. Zavala