Nonperturbative Evolution Equation for Quantum Gravity

TL;DR

The paper develops a nonperturbative renormalization group framework for quantum gravity using a scale-dependent effective action Γ_k that remains invariant under diffeomorphisms. By deriving an exact RG flow equation and enforcing modified Ward identities via the background-field method, it enables truncations like the Einstein–Hilbert truncation to yield nonperturbative flow of the gravitational couplings, notably G_k and λ_k. In 2+ε dimensions, it reveals a nontrivial UV fixed point for the rescaled Newton constant and shows λ_k–dependent corrections, while in four dimensions it demonstrates antiscreening, with G_k increasing at large distances, consistent with certain quantum gravity expectations. The approach offers a systematic, finite, and potentially extensible route to explore quantum gravity beyond perturbation theory, including IR and cosmological implications.

Abstract

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 BRS Ward--Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+epsilon dimensions, nonperturbative corrections to the beta--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.