HEAT KERNEL AND SCALING OF GRAVITATIONAL CONSTANTS

We consider the nonlocal energy-momentum tenser of quantum scalar and spinor fields in 2w-dimensional curved spaces. Working to lowest order in the curvature we show that, while the nonlocal terms proportional to square R, square square R, ..., square(w-2)R are fully determined b y the early-time behavior of the heat kernel, the terms proportional t o R depend on the asymptotic late-time behavior. This fact explains a discrepancy between the running of the Newton constant dictated by the RG equations and the quantum corrections to the Newtonian potential.