YANG-MILLS VACUUM-STRUCTURE AND QUANTUM-GRAVITY

Using renormalization group methods, we calculate the derivative expan sion of the effective Lagrangian for a covariantly constant gauge fiel d in curved spacetime. Curvature affects the vacuum; in particular it could induce phase transitions between different vacua. We also consid er the effect of quantum fluctuations of the metric, in the context of a renormalizable R(2) theory. In this case the critical curvature dep ends on the gravitational coupling constants.