FAMILY SYMMETRY, GRAVITY, AND THE STRONG CP PROBLEM

We show how in a class of models Peccei-Quinn symmetry can be realized as an automatic consequence of a gauged U(1) family symmetry. These models provide a solution to the strong CP problem either via a massless u-quark or via the DFSZ invisible axion. The local family symmetry protects against potentially large corrections to thetaBAR induced by quantum gravitational effects. In a supersymmetric extension, the ''mu-problem'' is shown to have a natural solution in the context of gravitationally induced operators. We also present a plausible mechanism which can explain the inter-generational mass hierarchy in such a context.