Nonperturbative Evolution Equation for Quantum Gravity

TL;DR

This paper introduces a nonperturbative, scale-dependent effective action for quantum gravity, deriving an exact evolution equation that describes its renormalization group flow, with applications to 2+epsilon and 4 dimensions.

Contribution

It presents a novel nonperturbative evolution equation for quantum gravity that is invariant under coordinate transformations and explores its implications in different dimensions.

Findings

Nonperturbative corrections to Newton's constant beta-function in 2+epsilon dimensions.

In 4D, Newton's constant exhibits antiscreening behavior, increasing at large distances.

The evolution equation maintains gauge invariance and satisfies Ward identities.

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.