Non-perturbative corrections to the gravitational effective action induced by a scalar field at finite and zero temperatures

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 nonperturbative contributions to the one-loop effective action are explicitly separated. The nonperturbative 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.