Semiclassical Gravity and Invisible Axions
  We show that charged Eguchi-Hanson instantons provide a concrete and calculable new source of intrinsic Peccei-Quinn symmetry breaking by quantum gravity. The size of this breaking is shown to depend sensitively on the short distance details of a given theory, but is generically suppressed by fermion zero modes. Demanding that these gravitational effects not affet the axion solution to the strong CP problem, we find that at least two sets of quarks with differing Peccei-Quinn charges are required. In addition, these effects obviate the cosmological axion domain wall problem but leave unchanged problems associated with coherent axion oscillations. 
R. Holman, T.W. Kephart and Soo-Jong REY