Should We Expect a Fixed Point for Newton's Constant?

Abstract

Newton's constant can be regarded as a wave function renormalization constant. As such, one would not expect it to approach a fixed point in the ultraviolet limit. We clarify why, due to the peculiar character of gravity, this expectation is incorrect. Moreover, the existence of a fixed point for Newton's constant, which has been discussed recently in the literature, suggests that gravity has a built-in UV cutoff when described in Planck units.