On the Ultraviolet Behaviour of Newton's constant

TL;DR

This paper discusses how Newton's constant scales in quantum gravity under the assumption of an ultraviolet fixed point, suggesting gravity may have an intrinsic UV cutoff in Planck units.

Contribution

It clarifies the scaling behavior of Newton's constant near an ultraviolet fixed point, highlighting implications for the UV properties of quantum gravity.

Findings

Newton's constant scales as inverse square of the cutoff

Existence of UV fixed point implies a built-in UV cutoff in Planck units

Gravity's UV behavior depends on the choice of units

Abstract

We clarify a point concerning the ultraviolet behaviour of the Quantum Field Theory of gravity, under the assumption of the existence of an ultraviolet Fixed Point. We explain why Newton's constant should to scale like the inverse of the square of the cutoff, even though it is technically inessential. As a consequence of this behaviour, the existence of an UV Fixed Point would seem to imply that gravity has a built-in UV cutoff when described in Planck units, but not necessarily in other units.