Vilkovisky unique effective action in quantum gravity

TL;DR

This paper calculates the divergent part of the one-loop Vilkovisky effective action in quantum Einstein gravity, confirming its independence from parametrization and conformal gauge choices, thus supporting its consistency.

Contribution

It provides the first explicit calculation of the Vilkovisky effective action's divergence in quantum gravity, demonstrating its gauge and parametrization independence.

Findings

Effective action divergence is parametrization-independent.

Effective action divergence is conformal gauge-independent.

Supports the consistency of Vilkovisky's approach in quantum gravity.

Abstract

The divergent part of the one-loop Vilkovisky unique effective action for quantum Einstein gravity is evaluated in the general parametrization of the quantum field, including the separated conformal factor. The output of this calculation explicitly demonstrates the parametrization and conformal gauge independence of the unique effective action with the configuration space metric chosen following Vilkovisky's prescription.