THE LARGE-DISTANCE LIMIT OF THE GRAVITATIONAL EFFECTIVE ACTION IN HYPERBOLIC BACKGROUNDS

The one-loop effective action for D-dimensional quantum gravity with n egative cosmological constant is investigated in spacetimes with compa ct hyperbolic spatial section. The explicit expansion of the effective action is derived as a power series of the curvature on the hyperboli c background, making use of heat-kernel and zeta-regularization techni ques. We discuss, at one-loop level, the Coleman-Weinberg-type suppres sion of the cosmological constant, proposed by Taylor and Veneziano.