Solutions to the strong CP problem in a world with gravity
  We examine the sensitivity of several solutions of the strong-CP problem to violations of global symmetries by Planck scale physics. We find that the Peccei-Quinn solution is extremely sensitive to U(1)_PQ violating operators of dimension less than 10. We construct models in which the PQ symmetry is protected by gauge symmetries to the requisite level. 
R. Holman, S.D.H. Hsu, T. Kephart, E. Kolb, R. Watkins and L. Widrow