Integrability and scheme independence of even-dimensional quantum geometry effective action (Q2774339)

In quantum gravity, the conformal anomalies constrain the form of the effective action. In even and odd number of dimensions, these are quite different. Therefore, the present paper restricts to the consideration in an even number of dimensions. NEWLINENEWLINENEWLINEThe functional integral is deduced, and the curvature squared terms of the effective action are calculated. It is shown, how the square of the D'Alembert-operator can be made conformally invariant by the addition of some curvature corrections. This fourth-order operator is used in the effective action. NEWLINENEWLINENEWLINEThen, the main application is to the 4 and 6 dimensional cases, and they are compared with the 2-dimensional one.