The derivative expansion in asymptotically safe quantum gravity: general setup and quartic order

TL;DR

This paper develops a comprehensive framework for analyzing the derivative expansion in asymptotically safe quantum gravity, focusing on mode decoupling, regularization, and fixed point structure at quartic order.

Contribution

It introduces a mode-decoupling and regularization framework applicable at any truncation order, and applies it to study the quartic order derivative expansion in quantum gravity.

Findings

Fixed point structure analyzed at quartic order

Framework ensures correct mode counting and regularization

Demonstrates applicability independent of truncation order

Abstract

We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling and cancellation of different modes in the Landau limit, and implements a correct mode count as well as a regularisation based on geometrical considerations. It is applicable independent of the truncation order. To illustrate the power of the framework, we discuss the quartic order of the derivative expansion and its fixed point structure as well as physical implications.