Heat Kernel and Scaling of Gravitational Constants

Abstract

We consider the non-local energy-momentum tensor of quantum scalar and spinor fields in $2w$-dimensional curved spaces. Working to lowest order in the curvature we show that, while the non-local terms proportional to $\square \mathcal{R}$, $\square \square \mathcal{R}$, $\dots ,{\square }^{w-2}\mathcal{R}$ are fully determined by the early-time behaviour of the heat kernel, the terms proportional to $\mathcal{R}$ depend on the asymptotic late-time behaviour. 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.

11 pages, latex file. Changes in the presentation and some references added

References in corpus (5)

• Leading Quantum Correction to the Newtonian Potential
• The Dark Matter Problem in Light of Quantum Gravity
• The basis of nonlocal curvature invariants in quantum gravity theory
• Asymptotic behaviours of the heat kernel in covariant perturbation theory
• Running Coupling Constants, Newtonian Potential and non localities in the Effective Action

Cited by in corpus (4)

• Nonperturbative Evolution Equation for Quantum Gravity
• Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
• On the running of the gravitational constant
• Nonlocal stress-energy tensor in time-dependent gravitational backgrounds