Running Coupling Constants, Newtonian Potential and non localities in the Effective Action

TL;DR

This paper derives quantum corrections to the Newtonian potential from a scalar field in curved spacetime, revealing logarithmic running of gravitational constants consistent with renormalization group predictions for specific couplings.

Contribution

It introduces a covariant, non-local effective action approach to compute quantum gravitational corrections on arbitrary backgrounds.

Findings

Logarithmic quantum corrections to Newtonian potential.

Identification of running gravitational constants.

Agreement with renormalization group predictions for certain couplings.

Abstract

We consider a quantum scalar field on an arbitrary gravitational background. We obtain the effective {\it in-in} equations for the gravitational fields using a covariant and non-local approximation for the effective action proposed by Vilkovisky and collaborators. {}From these equations, we compute the quantum corrections to the Newtonian potential. We find logarithmic corrections which we identify as the running of the gravitational constants. This running coincides with the renormalization group prediction only for minimal and conformal coupling.