Is there a $C$-function in 4D Quantum Einstein Gravity?

TL;DR

This paper proposes a functional renormalization group method to identify $C$-functions in 4D Quantum Einstein Gravity, aiming to extend concepts of conformal field theory to quantum gravity.

Contribution

It introduces a novel approach based on mode counting of the effective average action to find $C$-like functions in quantum gravity.

Findings

Method successfully applied to 4D Quantum Einstein Gravity

Demonstrates potential for identifying $C$-functions in quantum gravity

Provides a new tool for exploring asymptotic safety in gravity

Abstract

We describe a functional renormalization group-based method to search for `$C$-like' functions with properties similar to that in 2D conformal field theory. It exploits the mode counting properties of the effective average action and is particularly suited for theories including quantized gravity. The viability of the approach is demonstrated explicitly in a truncation of 4 dimensional Quantum Einstein Gravity, i.e. asymptotically safe metric gravity.