Ultraviolet Divergences and Scale-Dependent Gravitational Couplings

Abstract: 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 non-perturbative vacuum condensate. (Plenary Talk, 12-th Marcel Grossmann Conference on Recent Developments in General Relativity, Astrophysics and Relativistic Field Theories, UNESCO Paris, July 12-18, 2009).