Gauge dependence of momentum running in higher-derivative gravity

TL;DR

The paper shows that the momentum-running beta functions in higher-derivative gravity are explicitly gauge dependent, arising from nonlocal log(-□) contributions to the one-loop effective action. Using the background-field method for quadratic and conformal gravity, it distinguishes μ-running (gauge-invariant for local operators) from p-running (gauge-dependent due to nonlocal terms) and demonstrates that on-shell considerations are required to extract physical predictions. The authors argue that momentum-running alone cannot determine the UV behavior or asymptotic safety of the theories, and advocate computing on-shell scattering amplitudes to obtain gauge-invariant insights into high-energy gravity. These results caution against interpreting off-shell, background-field beta functions as physical observables and motivate further on-shell analyses of higher-derivative gravity theories.

Abstract

Recent works have argued that improved one-loop beta-functions capturing the physical momentum dependence of one-loop corrected higher-derivative gravity theories are the most suitable to describe their high-energy behaviour. This work critically tests the validity of this claim. We compute the explicit gauge dependence of the one-loop momentum running of curvature-squared operators in quadratic gravity and conformal gravity using the background field method. We find them to be gauge dependent, and we discuss the implications of this result for the theory and its physical predictivity.

Figures (1)

• Figure 1: Diagrams contributing to the 2-point function: bubbles (left) and tadpoles (right). The thin line can be the $h$ propagator or one of the ghosts, the thick line is the $f$ propagator, with momentum $p$.