Solutions to the strong-CP problem in a world with gravity

We examine various solutions of the strong-CP problem to determine their sensitivity to possible violations of global symmetries by Planck scale physics. While some solutions remain viable even in the face of such effects, violations of the Peccei-Quinn (PQ) symmetry by non-renormalizable operators of dimension less than 10 will generally shift the value of anti θ to values inconsistent with the experimental bound anti θ< or approx.10-9. We show that it is possible to construct axion models where gauge symmetries protect the PQ symmetry to the requisite level. (orig.)