Planck-scale corrections to axion models.

TLDR: If {ital d}=10, 11, or 12 these operators can solve the axion domain-wall problem, and this work describes a simple class of Kim-Shifman-Vainshtein-Zakharov axion models where this occurs.

Abstract: It has been argued that quantum gravitational effects will violate all nonlocal symmetries. Peccei-Quinn symmetries must therefore be an accidental'' or automatic consequence of local gauge symmetry. Moreover, higher-dimensional operators suppressed by powers of {ital M}{sub Pl} are expected to explicitly violate the Peccei-Quinn symmetry. Unless these operators are of dimension {ital d}{ge}10, axion models do not solve the strong {ital CP} problem in a natural fashion. A small gravitationally induced contribution to the axion mass has little if any effect on the density of relic axions. If {ital d}=10, 11, or 12 these operators can solve the axion domain-wall problem, and we describe a simple class of Kim-Shifman-Vainshtein-Zakharov axion models where this occurs. We also study the astrophysics and cosmology of heavy axions'' in models where 5{le}{ital d}{le}10.