Ultraviolet Divergences and Scale-Dependent Gravitational Couplings

I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely unrelated non-perturbative approaches, and how it relates to the vacuum state of quantum gravity, and specifically to the running of G. One distinctive feature of the new fixed point is the emergence of a second genuinely non-perturbative scale, analogous to the scaling violation parameter in non-abelian gauge theories. I argue that it is natural to identify such a scale with the small observed cosmological constant, which in quantum gravity can arise as a nonperturbative vacuum condensate. I then show how the lattice cutoff theory of gravity can in principle provide quantitative predictions on the running of G, which can then be used to construct manifestly covariant effective field equations, and from there estimate the size of non-local quantum corrections to the standard GR framework.