Quantum gravity and matter fields in a general background gauge

TL;DR

This paper investigates the gauge-dependence of the effective action in quantum gravity coupled with matter fields, confirming gauge independence on-shell and revealing the theory's non-renormalizability.

Contribution

It provides an explicit off-shell one-loop analysis in a general background gauge and confirms the DeWitt-Kallosh theorem's implications.

Findings

Effective action reduces to known results in specific gauges.

On-shell effective action is gauge-independent.

The theory is non-renormalizable in a general background gauge.

Abstract

We analyse the gauge-dependence of the effective action in an interacting quantum theory of gravitational and matter fields. An explicit off-shell result is obtained in a general background gauge at one-loop order, which reduces in a particular gauge to the effective action found by 't Hooft-Veltman. We confirm the validity of DeWitt-Kallosh theorem, which implies that the on-shell effective action should be independent of the gauge-fixing parameter. We employ this theorem to expose the non-renormalizability of the theory in a general background gauge.