Conformal quantum gravity with the Gauss-Bonnet term

Conformal gravity is one of the most important models of quantum gravity with higher derivatives. We investigate the role of the Gauss-Bonnet term in this theory. The coincidence limit of the second coefficient of the Schwinger-DeWitt expansion is evaluated in an arbitrary dimension n. In the limit $n=4$ the Gauss-Bonnet term is topological and its contribution cancels. This cancellation provides an efficient test for the correctness of calculation and, simultaneously, clarifies the long-standing general problem concerning the role of the topological term in quantum gravity. For n≠4 the Gauss-Bonnet term becomes dynamical in the classical theory and relevant at the quantum level. In particular, the renormalization group equations in dimension n=4-ε manifest new fixed points due to quantum effects of this term.