Nonperturbative evolution equation for quantum gravity

A scale-dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified Becchi-Rouet-Stora Ward identities. The evolution equation is solved for a simple truncation of the space of actions. In $2+\varepsilon$ dimensions, nonperturbative corrections to the β function of Newton’s constant are derived and its dependence on the cosmological constant is investigated. In 4 dimensions, Einstein gravity is found to be “antiscreening;” i.e., Newton’s constant increases at large distances.