Does the Vilkovisky-De Witt effective action in quantum gravity depend on the configuration space metric?

Abstract

The dependence on the configuration space metric of the Vilkovisky-De Witt effective action in quantum gravity is discussed. As an example d-dimensional Einstein gravity on the flat background R d or R k× T d−k is considered, where the one-loop Vilkovisky-De Witt effective action with the one-parameter dependent configuration space metric is calculated. The dependence on the configuration space metric of the Vilkovisky-De Witt EA in gravity on the space R 4× S 1 has been investigated for the first time by Huggins, Kunstatter, Leivo and Toms.