Non-perturbative corrections to the one-loop free energy induced by a massive scalar field on a stationary slowly varying in space gravitational background

TL;DR

This paper derives explicit non-perturbative corrections to the one-loop gravitational effective action caused by a massive scalar field in stationary, slowly varying gravitational backgrounds, highlighting differences between perturbative and non-perturbative parts.

Contribution

It provides explicit formulas for non-perturbative corrections at zero and finite temperatures, and distinguishes their dependence on the Killing vector and covariant structures.

Findings

Perturbative part matches known large mass expansion.

Non-perturbative part depends explicitly on the Killing vector.

Non-perturbative corrections cannot be expressed covariantly in terms of metric alone.

Abstract

The explicit expressions for the one-loop non-perturbative corrections to the gravitational effective action induced by a scalar field on a stationary gravitational background are obtained both at zero and finite temperatures. The perturbative and non-perturbative contributions to the one-loop effective action are explicitly separated. It is proved that, after a suitable renormalization, the perturbative part of the effective action at zero temperature can be expressed in a covariant form solely in terms of the metric and its derivatives. This part coincides with the known large mass expansion of the one-loop effective action. The non-perturbative part of the renormalized one-loop effective action at zero temperature is proved to depend explicitly on the Killing vector defining the vacuum state of quantum fields. This part cannot be expressed in a covariant way through the metric and its derivatives alone. The implications of this result for the structure and symmetries of the effective action for gravity are discussed.