Renormalisation of Newton's constant

Abstract

The problem of obtaining a gauge independent beta function for Newton's constant is addressed. By a specific parameterisation of metric fluctuations a gauge independent functional integral is constructed for the semiclassical theory around an arbitrary Einstein space. The effective action then has the property that only physical polarisations of the graviton contribute, while all other modes cancel with the functional measure. We are then able to compute a gauge independent beta function for Newton's constant in $d$-dimensions to one-loop order. No Landau pole is present provided $N_g < 18$, where $N_g = d(d-3)/2$ is the number of polarisations of the graviton. While adding a large number of matter fields can change this picture, the absence of a pole persists for the particle content of the standard model in four spacetime dimensions.