Exact RG Flow Equations and Quantum Gravity

TL;DR

This paper compares different functional renormalization group equations, proposing a generalized background field version that better supports Weinberg's asymptotic safety approach to quantum gravity, backed by heat kernel analysis.

Contribution

It introduces a new background field RG equation closely related to the Polchinski equation, tailored for quantum gravity asymptotic safety studies.

Findings

The generalized background field RG equation is more suitable for quantum gravity.

Heat kernel expansion supports the asymptotic safety scenario.

Evidence aligns with previous research on quantum gravity RG flows.

Abstract

We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.