Planck-Scale Physics and the Peccei-Quinn Mechanism
  Global-symmetry violating higher-dimension operators, expected to be induced by Planck-scale physics, in general drastically alter the properties of the axion field associated with the Peccei-Quinn solution to the strong-CP problem, and render this solution unnatural. The particle physics and cosmology associated with other global symmetries can also be significantly changed. 
Marc Kamionkowski and John March-Russell