Functional renormalization group approach and gauge dependence in gravity theories

TL;DR

This paper examines how gauge fixing influences the effective average action in quantum gravity models, revealing that regulator choices can preserve background symmetry but still lead to gauge dependence due to BRST non-invariance.

Contribution

It identifies conditions under which the background field symmetry is preserved and highlights the persistent gauge dependence caused by regulator non-invariance in quantum gravity.

Findings

Background symmetry can be preserved with specific regulator functions.

Gauge dependence persists due to non-invariance of regulator action under BRST.

Gauge fixing dependence remains even on-shell, affecting quantum gravity calculations.

Abstract

We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless the gauge symmetry is preserved at the quantum level, the non-invariance of the regulator action under the global BRST transformations leads to the gauge fixing dependence even under the use of the on-shell conditions.