Abstract
The one-loop unique effective action by Vilkovisky in the d = 5 Einstein gravity and R 2-gravity on the space M 4×S 1 is calculated, where M 4 is the Minkowski space and S 1 is a one-dimensional sphere. Also, the one-loop unique effective action for d-dimensional Einstein gravity on M 4×T d−4 is calculated. The results of the calculation of the standard effective action are compared with those in the same theories.
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