Functional renormalization group approach and gauge dependence in gravity theories

Vítor F Barra,Tibério De Paula Netto,Peter M Lavrov,Ilya L Shapiro,Eduardo Antonio Dos Reis

doi:10.1103/physrevd.101.065001

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.

Highlights

The interest in the nonperturbative formulation in quantum gravity has two strong motivations
Regardless if the gauge symmetry is preserved at the quantum level, the noninvariance of the regulator action under the global BRST transformations leads to the gauge-fixing dependence even under the use of the on-shell conditions
We explored the problem of gauge invariance and the gauge-fixing dependence using the background field formalism, for gravity theories in the functional renormalization group (FRG) framework

Summary

INTRODUCTION

The interest in the nonperturbative formulation in quantum gravity has two strong motivations. We apply the background field method [41,42,43] (recent advances for the gauge theories can be found in [16,44,45,46,47,48,49] and discussion for the quantum gravities case in [50]) in the FRG approach as a reformulation to the quantization procedure for quantum gravity theories to study the gauge dependence problem in this kind of theory. The Grassmann parity of a quantity A is denoted as εðAÞ

QUANTUM GRAVITY IN THE BACKGROUND FIELD FORMALISM

FRG APPROACH FOR QUANTUM GRAVITY THEORIES

GAUGE DEPENDENCE OF EFFECTIVE AVERAGE ACTION

CONCLUSIONS AND PERSPECTIVES